Personal Data

Full name

Luis Fernando Sanchez Rodrigues

Publishing name

Luis Fernando Sanchez Rodrigues

Birthday

1948-11-27T00:00:00

Academic Degrees

DOUTORAMENTO(0)

Degree date

1981

Final grade

aprovado, distinção e louvor

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

Supervisor

Co-supervisor

Scientific area

AGREGAÇÃO(0)

Degree date

1989

Final grade

aprovado

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

Supervisor

Co-supervisor

Scientific area

Profissional activity

Period Position Institution
1971-1973 Assistente eventual Faculdade de Ciências da Universidade de Lisboa
1973-1981 Assistente Faculdade de Ciências da Universidade de Lisboa
1981-1985 Professor Auxiliar Faculdade de Ciências da Universidade de Lisboa
1985-1990 Professor Associado/Associate Professor Faculdade de Ciências da Universidade de Lisboa
1990- Professor catedrático / Professor Faculdade de Ciências da Universidade de Lisboa

Area of scientific activity

Area of scientific activity

Ordinary Differential Equations (boundary value problems)<br>Nonlinear Analysis

Specialization domain

Ordinary Differential Equations: boundary value problems, singular problems, topological and variational methods.

Current main scientific area

Research on heteroclinic solutions in 2nd and 4th order problems.<br>Singular equations arising from elliptic boundary value problems.<br>Equations with nonlocal terms.<br>Boundary value problems for 4th order ODEs.<br>Boundary value problems in unbounded intervals.

Other scientific activities

-

Experience as scientific advisor

Several master thesis.

PhD´s:
M. Rosário Grossinho (Universidade de Lisboa, 1998).
To Fu Ma (Universidade de Lisboa, 1995).
José Maria Gomes (Universidade de Lisboa, 2005).
Ricardo Enguiça (Universidade de Lisboa, Julho de 2011.)

Supervision of post-doctoral student Sunra Mosconi (Sept-Dec 2012) in Project PTDC/MAT/113383/2009.

Participations in R&D projects

As coordinator: 1) "Modelos matemáticos em ressonância" (acção integrada luso-espanhola, 1986/7); 2) "Problemas não lineares em ressonância" (contrato JNICT 87589, 1988-89; 3) "Problemas semilineares com estrutura variacional" (contrato STRIDE STRDA 531/92, 1993-94); 4) "Non linear boundary value problems: existence, multiplicity, bifurcation and stability of solutions" (Human capital and mobility CHRX-CT94-0555), 1994-97 (coordinator of the Portuguese team); 5); 5) Problemas de valores fronteira não lineares (acção integrada luso-espanhola, 2000/2001). 6) Dinâmica não linear em Mecânica e em Biologia (acção integrada luso-espanhola, 2001/2002). 7) Centro de Matemática e Aplicações Fundamentais - coordinator since April 2004.

Educational Project: coordinator (with A. Machado) of the project REANIMAT sponsored by Fundação Calouste Gulbenkian - a three-year experiment in the teaching of Mathematics at secondary level, 2001/2004.

As participant: Project PTDC/MAT/113383/2009 (P. I. Alessandro Margheri).
Project PTDC/MAT/115168/2009 (P. I. Nico Stollenwerk).

Awards

Year Award Awarding entity

Publications

Livros (editor)

  • 1. Equadiff 95 - International Conference on Differential Equations, L. Magalhães, C. Rocha and L. Sanchez (eds), World Scientific 1998.<br>2. Nonlinear Analysis and its Applications to Differential Equations, Progress in Nonlinear Differential Equations and their Applications, vol. 43, Birkhauser 2001, M.R. Grossinho, M. Ramos, C. Rebelo and L. Sanchez (eds)<br>

Publicações em actas de encontros científicos

  • 1. L. Sanchez, A note on periodic solutions of heat equation with a superlinear term, in Nonlinear Functional Analysis and Fixed Point Theory, ed. S. P. Singh, Reidel, Dordrecht 1986.
    2. P. Habets, M. Ramos and L. Sanchez, Jumping nonlinearity for 2. order ODEs with positive forcing, in Delay Differential Equations and Dynamical Systems, eds. S. Busenberg and M. Martelli, Lecture Notes in Mathematics, 1475 (1991), 191-203.
    3. P. Habets, M. Ramos and L. Sanchez, Solutions of prescribed sign for BVPs with asymmetric nonlinearities, in International Conference on Differential Equations, ed. C. Perelló, C. Simó and J. Solà-Morales, World Scientific, 1993, 584-588.
    4. L. Sanchez, Heteroclinic connections for a class of non-autonomous systems, USA-ChileWorkshop
    on Nonlinear Analysis, Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 257-266.
    5. J. M. Gomes and L. Sanchez, Positive solutions of a Singular Ordinary Differential Equation relevant in Mathematical Physics, in The First 60 Years of Nonlinear Analysis of Jean Mawhin, eds M Delgado, J López-Gómez, R Ortega and A Suárez, World Scientific, 89-102 (2004).
    6. D. Bonheure, J. M. Gomes and L. Sanchez, Positive solutions of a second order singular ordinary differential equation, Equadiff 2003, Dumortier, Broer, Mawhin, Vanderbauwhede, Lunel, eds, World Scientific 2005, 234-236.
    7. A. Gavioli and L. Sanchez, On Bounded Trajectories for Some Non-Autonomous Systems, in Differential Equations, Chaos and Variational Problems, Series: Progress in Nonlinear Differential Equations and Their Applications , Vol. 75, 2008, Staicu, Vasile (Ed.) 211-222.
    8. R. Enguiça and L. Sanchez, A second order non-autonomous problem on the half-line: a variational approach, in Mathematical models in engineering, Biology and Medicine, AIP Conference Proceedings, Melville 2009, A. Cabada, E. Liz and J. J. Nieto (eds.), 119-128.

Capítulos de livros

  • J. P. Dias, M. Figueira and L. Sanchez, Formation of singularities for the solutions of some quasilinear wave equations, in "Équations aux dérivées partielles et applications", Articles dédiés à J.-L. Lions, Elsevier, Paris, 1998.

Capítulos de livros

  • D. Bonheure and L. Sanchez, Heteroclinic orbits for some classes of second and fourth order differential equations, Handbook of Differential Equations: Ordinary Differential Equations, vol. 3, 103-202, A. Cañada, P. Drabek, A. Fonda, editors, Elsevier 2006.

Artigos em revistas de circulação internacional com arbitragem científica

  • 56. Andrea Gavioli and Luís Sanchez, Positive homoclinic solutions to some Schrödinger type equations, Differential and Integral Equations 29 (2016), 665-682.

    55. Andrea Gavioli, L. Sanchez, A variational property of critical speed to travelling waves in the presence of nonlinear diffusion, Applied Mathematical Letters, 48 (2015), 47-54.

    54. Maurizio Garrione, Luís Sanchez, Monotone traveling waves for reaction-diffusion equations involving the curvature operator, Boundary Value Problems 2015, 2015:45

    53. Coelho, Isabel; Sanchez, Luís Travelling wave profiles in some models with nonlinear diffusion. Appl. Math. Comput. 235 (2014), 469–481.

    52. Denis Bonheure, José Ángel Cid, Colette De Coster and Luís Sanchez, Heteroclinics for some non autonomous third order differential equations, Topological Methods in Nonlinear Analysis 43 (2014) 53-68.

    51. Ricardo Enguiça, Andrea Gavioli and Luís Sanchez, A class of singular first order differential equations with applications in reaction-diffusion, Discrete and Continuous Dynamical Systems - Series A, 33 (2013), 173 – 191.

    50. Alberto Cabada, J. Ángel Cid, and Luís Sanchez, Existence of Solutions for Elliptic Systems with Nonlocal Terms in One Dimension, Boundary Value Problems, Volume 2011 (2011), Article ID 518431, 12 pages.

    49. R. Enguiça, A. Gavioli and L. Sanchez, Solutions of second-order and fourth-order ODEs on the half-line, Nonlinear Analysis: Theory, Methods & Applications 73 ( 9), 2010, 2968-2979.

    48. A. Gavioli and L. Sanchez, Heteroclinics for non-autonomous second order differential equations, Differential and Integral Equations 22, 999-1018 (2009).

    47. A. Gavioli and L. Sanchez, On a class of bounded trajectories for some non-autonomous Systems, Math. Nachr. 281, No. 11, 1557 – 1565 (2008).

    46. R. Enguiça and L. Sanchez, A nonlocal maximum principle and applications, Communications in Applied Nonlinear Analysis, Volume 15 (2008), Number 1, 1–17.

    45. Ricardo Enguica, Luis Sanchez, Existence and localization of solutions for fourth-order boundary-value problems, Electr. J. Diff. Equations Vol. 2007(2007), No. 127 pp. 1-10.

    44. P. Habets and L. Sanchez, A monotone method for fourth order boundary value problems involving a factorizable linear operator, Portugaliae Mathematica 64 (2007), 255-279.

    43. J. Angel Cid, A. Cabada and L. Sanchez, Positivity and lower and upper solutions for fourth order boundary value problems, Nonlinear Analysis Series A: Theory, Methods & Applications 67 (2007) 1599–1612.

    42. R. Enguiça and L. Sanchez, Radial solutions for a nonlocal boundary value problem, Boundary Value Problems 2006, Art. ID 32950, 18 pp.

    41. J. M. Gomes and L. Sanchez, On a variational approach to some non-local boundary value problems, Applicable Analysis 84 (2005), 909-925.

    40. D. Bonheure, J. M. Gomes and L. Sanchez, Positive solutions of a second order singular ordinary differential equation, Nonlinear Analysis T.M.A. 61 (2005), 1383-1399.

    39. M. R. Grossinho, L. Sanchez and S. A. Tersian, On the solvability of a boundary value problem for a 4th order ordinary differential equation, Applied Mathematics Letters 18 (4) 2005, 439-444.

    38. J. M. Gomes and L. Sanchez, A variational approach to some boundary value problems in the half-line, Z.angew.Math.Phys. 56 (2005) 192-209.

    37. D. Bonheure, P. Habets and L. Sanchez, Heteroclinics for fourth order symmetric bistable equations, Atti del Seminario Matematico e Fisico dell’Università Modena e Reggio Emilia, LII, (2004) 213-227.

    36. M. Arias, J. Campos, A. Robles-Pérez and L. Sanchez, Fast and heteroclinic solutions for a second order ODE related to Fisher- Kolmogorov’s equation, Calculus of Variations and Partial Differential Equations, 21 (2004), 319-334.

    35. J. Ángel Cid and L. Sanchez, Periodic solutions for second order differential equations with discontinuous restoring forces, J. Math. Anal. Appl. 288 (2003), 349-364.

    34. J. Chaparova and L. Sanchez, A variational approach for a generalized Emden-Fowler equation, Applicable Analysis 82, 1003-1016 (2003).

    33. D. Bonheure, L. Sanchez, M. Tarallo and S. Terracini, Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equations, Calculus of Variations and Partial Differential Equations 17, 341-356 (2003).

    32. A. Cabada and L. Sanchez, Second Order Singular Periodic Problems in Presence of Dry Friction, Proc. Amer. Math. Society 131, 2137-2144 (2003).

    31. L. Sanchez, A note on a nonautonomous ODE related to the Fisher equation, J. Comput. Appl. Math. 113 (2000), 201-209.

    30. J. P. Dias, M. Figueira and L. Sanchez, On the existence of schock fronts for a Burgers equation with a singular source term, Mathematical Methods in the Applied Sciences 21 (1998), 1107-1113.

    29. L. Sanchez, Second order systems of ODE's related to a Ginzburg-Landau model, Applicable Analysis 67 (1997), 59-72.

    28. To Fu Ma, M. Ramos and L. Sanchez, Multiple solutions for a class of boundary value problems near resonance: a variational approach, Nonlinear Analysis, T.M.A. 30(6), 3301-3311 (1997).

    27. M. Ramos and L. Sanchez, A variational approach to multiplicity in elliptic problems near resonance, Proc. Royal Soc. Edinburgh 127A (1997), 385-394.

    26. A. Cabada and L. Sanchez, A positive operator approach to the Neumann problem for a second order ordinary differential equation, J. Math. Anal. Applications 204 (1996), 774 - 785.

    25. P. Habets and L. Sanchez, A two-point problem with nonlinearity depending only of the derivative, SIAM J. Math. Analysis 28 (1997), 1205-1211.

    24. To Fu Ma and L. Sanchez, Three solutions of a quasilinear elliptic problem near resonance, Math. Slovaca 47 (1997), 451-457.

    23. J. Matos and L. Sanchez, Two solutions for a nonlinear Dirichlet problem with positive forcing, Math. Bohemica 121, n. 1 (1996), 41-54.

    22. M. Ramos and L. Sanchez, Homotopical linking and Morse index estimates in min-max theorems, Manuscripta Math. 87(1995), 269-284.

    21. C. Rebelo and L. Sanchez, Existence and multiplicity for an ODE with nonlinear boundary conditions, Differential Equations and Dynamical Systems, 3 (1995), 383-396.

    20. To Fu Ma and L. Sanchez, A note on resonance problems with nonlinearity bounded in one direction, Bull. Austr. Math. Soc., 52 (1995), 183-188.

    19. G. Dinca and L. Sanchez, Multiple solutions of boundary value problems: an elementary approach via the shooting method, Nonlinear Differential Equations and Applications, 1(1994), 163-178.

    18. L. Sanchez, A note on nontrivial periodic solutions of dynamical systems with subquadratic potential, Rev. Mat. Univ. Complutense de Madrid, 7(1994), 179-193.

    17. C. De Coster and L. Sanchez, Upper and lower solutions, Ambrosetti-Prodi problem and positive solutions for fourth order ODE, Rivista di Matematica Pura ed Applicata, 14 (1994), 57-82.

    16. P. Habets, M. Ramos and L. Sanchez, Jumping nonlinearities for Neumann BVPs with positive forcing, Nonlinear Analysis TMA 20 (1993), 533-549.

    15. L. Sanchez, Positive solutions for a class of semilinear two-point BVPs, Bull. Austr. Math. Soc. 45(1992), 439-451.

    14. L. Sanchez, Boundary value problems for some fourth order ODEs, Applicable Analysis 38 (1990), 161-177.

    13. P. Habets and L. Sanchez, Periodic solutions of dissipative dynamical systems with singular potentials, Differential and Integral Equations, 3 (1990), 1139-1149.

    12. P. Habets and L. Sanchez, Periodic solutions of some Liénard equations with singularities, Proc. Amer. Math. Soc. 109 (1990), 1035-1044.

    11. M. Ramos and L. Sanchez, Variational elliptic problems involving noncoercive functionals, Proceedings of the Royal Soc. Edinburgh, 112A (1989), 177-185.

    10. M. Ramos and L. Sanchez, Multiple periodic solutions of some nonlinesr differential equations of higher order, Differential and Integral Equations, 2 (1989), 81-90.

    9. C. P. Gupta, J. J. Nieto and L. Sanchez, Periodic solutions of some Liénard and Duffing equations, J. Math. Anal. Applications, 140 (1989), 67-82.

    8. J. J. Nieto and L. Sanchez, Periodic boundary value problem for some Duffing equations, Differential and Integral Equations, 1 (1988), 399-408.

    7. L. Sanchez, Resonance problems with nonlinearity interfering with eigenvalues of higher order, Applicable Analysis 25, (1987), 275-286.

    6. M. R. Grossinho and L. Sanchez, A note on periodic solutions of some nonautonomous differential equations, Bull. Austr. Math. Soc. 34 (1986), 253-265.

    5. K. C. Chang and L. Sanchez, Nontrivial periodic solutions of a nonlinear beam equation, Math. Meth. in the Appl. Sci. 4 (1982), 194-205.

    4. A. Bahri and L. Sanchez, Periodic solutions of a nonlinear telegraph equation, B.U.M.I. 18B (1981), 709-720.

    3. L. Sanchez, Periodic solutions of a nonlinear evolution equation with a linear dissipative term, Rend. Sem. Mat. Univ. Politecn. Torino, 37 (1980), 183-191.

    2. L. Sanchez, Solutions périodiques non triviales d'une équation d'évolution non linéaire du quatrième ordre, C. R. Acad. Sci. Paris série A, 280 (1980), 305-307.

    1. L. Sanchez, A note on a differential equation of the dynamics of wires, B.U.M.I. 16A, (1979), 391-397.









Teses

  • <br>

Teses

Teses

  • Soluções periódicas de certas equações diferenciais não lineares, dissertação de doutoramento, UNiversidade de Lisboa 1981.

Artigos em revistas nacionais com arbitragem científica

  • Simão Correia e Luís Sanchez, Ondas progressivas no modelo de Fisher-Kolmogorov - um clássico moderno, Bol. Soc. Port. Mat. No. 67 (2012), 165–184.

Livros (autor)

  • L. Sanchez, Métodos da teoria de pontos críticos, Textos de Matemática, Faculdade de Ciências da Universidade de Lisboa, 1993.

Communications

Outras comunicações orais

1. Nontrivial periodic solutions of some nonlinear evolution equations, Workshop on nonlinear boundary value problems, SISSA, Trieste, 1980.<br>2. Remarks on some nonlinear heat equations, Nonlinear Functional Analysis and Fixed Point Theory, Maratea, 1985.<br>3. Boundary value problems for some nonlinear beam equations, Gewonlische Differentialgleichungen, Oberwolfach, 1989.<br>4. Positive solutions for some semilinear two-point BVPs, Conference on Boundary Value Problems for Ordinary Differential Equations, Athens, Ohio, Junho 1990.<br>5. An elementary approach to multiplicity results for a class of boundary value problems, Equadiff 8, Bratislava 1993.<br>6. Multiple solutions for a class of boundary value problems near resonance: a variational approach, WCNA 96, Athens, July 1996.<br>7. Heteroclinics for some conservative 4th order ordinary differential equations, Equadiff 10, Prague 2001.<br>8. Nonlocal maximum principles and applications, Univ. Modena, Novembro 2006.<br>

Comunicações orais por convite

Comunicações orais por convite

1. Boundary value problems in unbounded intervals for a class of non-autonomous ordinary differential equations, USACHILE, Viña del Mar, January 2000.
2. On a singular boundary value problem relevant in Mathematical Physics, Homenaje a Jean Mawhin, Sevilla,April 2003.
3. A variational approach to positive solutions of second order singular ODE´s, Seminar on differential equations and integration theory, Mathematical Institute, Prague, May 2003.
4. Positive solutions of a second order singular ordinary differential equation, International Workshop on Analysis and Numerical Approximation of Singular Problems, IST, Lisboa, November 2004.
5. On some classical boundary value problems in the half line - a variational approach,Trends in Differential Equations and Dynamical Systems, Università degli Studi di Modena e Reggio Emilia, Reggio Emilia september 2005.
6. On bounded trajectories of some non-autonomous systems, Views on ODEs, Univ. Aveiro, Junho 2006.
7. On bounded trajectories for some non-autonomous Systems, 1st Iberian mathematical meeting, Lisboa, Fevereiro 2007.
8.Heteroclinics for some non-autonomous second order differential equations, Nonlinear Differential Equations – A tribute to the work of Patrick Habets & Jean Mawhin, Brussels September 2008.
9. Heteroclinics for some non-autonomous second order differential equations, Conference on Boundary Value Problems, Santiago de Compostela, September 2008.
10. On some variational problems for second and fourth order non autonomous equations in unbounded intervals, Second Meeting IST-IME, Lisboa, September 2009.
11. Heteroclinics for u’’’=f(u), 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden, May 2010.
12. A 1st order equation with applications in reaction-diffusion, International Conference on Differential & Difference Equations and Applications, Ponta Delgada, Julho 2011.
13. Travelling Waves and Critical Speed in Equations of Fisher-Kolmogorov type, Intensive two-month on boundary value problems for differential equations, Università di M odena e Reggio Emilia, June 2012.
14. Heteroclinics and other Solutions in Unbounded Intervals for Third and
Fourth Order ODEs, Intensive two-month on boundary value problems for differential equations, Università di M odena e Reggio Emilia, June 2012.
15. Travelling waves and their critical speed in FKPP equations, WOAT 2012, Instituto Superior Técnico, Lisboa, September 2012.
16. Travelling waves and critical speed for some models with nonlinear diffusion, Qualitative Theory of Nonlinear Differential Equations, Univ. Trieste, 30 Jan-1 Febr 2013.
17. . “Heteroclinics for some 2nd, 3rd and 4th order differential equations” and “Travelling waves for FKPP equations, critical speed and nonlinear diffusion” – two talks at a mini-school on Differential Equations held at the Mathematical Institute of the Czech Academy of Sciences, Brno branch, May 2013.