Personal Data
Full name
Luis Fernando Sanchez Rodrigues
Publishing name
Luis Fernando Sanchez Rodrigues
Birthday
19481127T00:00:00
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
Cosupervisor
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
Cosupervisor
Scientific area
Profissional activity
Period  Position  Institution 

19711973  Assistente eventual  Faculdade de Ciências da Universidade de Lisboa 
19731981  Assistente  Faculdade de Ciências da Universidade de Lisboa 
19811985  Professor Auxiliar  Faculdade de Ciências da Universidade de Lisboa 
19851990  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 postdoctoral student Sunra Mosconi (SeptDec 2012) in Project PTDC/MAT/113383/2009.
Participations in R&D projects
As coordinator: 1) "Modelos matemáticos em ressonância" (acção integrada lusoespanhola, 1986/7); 2) "Problemas não lineares em ressonância" (contrato JNICT 87589, 198889; 3) "Problemas semilineares com estrutura variacional" (contrato STRIDE STRDA 531/92, 199394); 4) "Non linear boundary value problems: existence, multiplicity, bifurcation and stability of solutions" (Human capital and mobility CHRXCT940555), 199497 (coordinator of the Portuguese team); 5); 5) Problemas de valores fronteira não lineares (acção integrada lusoespanhola, 2000/2001). 6) Dinâmica não linear em Mecânica e em Biologia (acção integrada lusoespanhola, 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 threeyear 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), 191203.
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. SolàMorales, World Scientific, 1993, 584588.
4. L. Sanchez, Heteroclinic connections for a class of nonautonomous systems, USAChileWorkshop
on Nonlinear Analysis, Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 257266.
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 LópezGómez, R Ortega and A Suárez, World Scientific, 89102 (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, 234236.
7. A. Gavioli and L. Sanchez, On Bounded Trajectories for Some NonAutonomous Systems, in Differential Equations, Chaos and Variational Problems, Series: Progress in Nonlinear Differential Equations and Their Applications , Vol. 75, 2008, Staicu, Vasile (Ed.) 211222.
8. R. Enguiça and L. Sanchez, A second order nonautonomous problem on the halfline: 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.), 119128.
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, 103202, 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), 665682.
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), 4754.
54. Maurizio Garrione, Luís Sanchez, Monotone traveling waves for reactiondiffusion 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) 5368.
51. Ricardo Enguiça, Andrea Gavioli and Luís Sanchez, A class of singular first order differential equations with applications in reactiondiffusion, 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 secondorder and fourthorder ODEs on the halfline, Nonlinear Analysis: Theory, Methods & Applications 73 ( 9), 2010, 29682979.
48. A. Gavioli and L. Sanchez, Heteroclinics for nonautonomous second order differential equations, Differential and Integral Equations 22, 9991018 (2009).
47. A. Gavioli and L. Sanchez, On a class of bounded trajectories for some nonautonomous 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 fourthorder boundaryvalue problems, Electr. J. Diff. Equations Vol. 2007(2007), No. 127 pp. 110.
44. P. Habets and L. Sanchez, A monotone method for fourth order boundary value problems involving a factorizable linear operator, Portugaliae Mathematica 64 (2007), 255279.
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 nonlocal boundary value problems, Applicable Analysis 84 (2005), 909925.
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), 13831399.
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, 439444.
38. J. M. Gomes and L. Sanchez, A variational approach to some boundary value problems in the halfline, Z.angew.Math.Phys. 56 (2005) 192209.
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) 213227.
36. M. Arias, J. Campos, A. RoblesPérez 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), 319334.
35. J. Ángel Cid and L. Sanchez, Periodic solutions for second order differential equations with discontinuous restoring forces, J. Math. Anal. Appl. 288 (2003), 349364.
34. J. Chaparova and L. Sanchez, A variational approach for a generalized EmdenFowler equation, Applicable Analysis 82, 10031016 (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, 341356 (2003).
32. A. Cabada and L. Sanchez, Second Order Singular Periodic Problems in Presence of Dry Friction, Proc. Amer. Math. Society 131, 21372144 (2003).
31. L. Sanchez, A note on a nonautonomous ODE related to the Fisher equation, J. Comput. Appl. Math. 113 (2000), 201209.
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), 11071113.
29. L. Sanchez, Second order systems of ODE's related to a GinzburgLandau model, Applicable Analysis 67 (1997), 5972.
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), 33013311 (1997).
27. M. Ramos and L. Sanchez, A variational approach to multiplicity in elliptic problems near resonance, Proc. Royal Soc. Edinburgh 127A (1997), 385394.
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 twopoint problem with nonlinearity depending only of the derivative, SIAM J. Math. Analysis 28 (1997), 12051211.
24. To Fu Ma and L. Sanchez, Three solutions of a quasilinear elliptic problem near resonance, Math. Slovaca 47 (1997), 451457.
23. J. Matos and L. Sanchez, Two solutions for a nonlinear Dirichlet problem with positive forcing, Math. Bohemica 121, n. 1 (1996), 4154.
22. M. Ramos and L. Sanchez, Homotopical linking and Morse index estimates in minmax theorems, Manuscripta Math. 87(1995), 269284.
21. C. Rebelo and L. Sanchez, Existence and multiplicity for an ODE with nonlinear boundary conditions, Differential Equations and Dynamical Systems, 3 (1995), 383396.
20. To Fu Ma and L. Sanchez, A note on resonance problems with nonlinearity bounded in one direction, Bull. Austr. Math. Soc., 52 (1995), 183188.
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), 163178.
18. L. Sanchez, A note on nontrivial periodic solutions of dynamical systems with subquadratic potential, Rev. Mat. Univ. Complutense de Madrid, 7(1994), 179193.
17. C. De Coster and L. Sanchez, Upper and lower solutions, AmbrosettiProdi problem and positive solutions for fourth order ODE, Rivista di Matematica Pura ed Applicata, 14 (1994), 5782.
16. P. Habets, M. Ramos and L. Sanchez, Jumping nonlinearities for Neumann BVPs with positive forcing, Nonlinear Analysis TMA 20 (1993), 533549.
15. L. Sanchez, Positive solutions for a class of semilinear twopoint BVPs, Bull. Austr. Math. Soc. 45(1992), 439451.
14. L. Sanchez, Boundary value problems for some fourth order ODEs, Applicable Analysis 38 (1990), 161177.
13. P. Habets and L. Sanchez, Periodic solutions of dissipative dynamical systems with singular potentials, Differential and Integral Equations, 3 (1990), 11391149.
12. P. Habets and L. Sanchez, Periodic solutions of some Liénard equations with singularities, Proc. Amer. Math. Soc. 109 (1990), 10351044.
11. M. Ramos and L. Sanchez, Variational elliptic problems involving noncoercive functionals, Proceedings of the Royal Soc. Edinburgh, 112A (1989), 177185.
10. M. Ramos and L. Sanchez, Multiple periodic solutions of some nonlinesr differential equations of higher order, Differential and Integral Equations, 2 (1989), 8190.
9. C. P. Gupta, J. J. Nieto and L. Sanchez, Periodic solutions of some Liénard and Duffing equations, J. Math. Anal. Applications, 140 (1989), 6782.
8. J. J. Nieto and L. Sanchez, Periodic boundary value problem for some Duffing equations, Differential and Integral Equations, 1 (1988), 399408.
7. L. Sanchez, Resonance problems with nonlinearity interfering with eigenvalues of higher order, Applicable Analysis 25, (1987), 275286.
6. M. R. Grossinho and L. Sanchez, A note on periodic solutions of some nonautonomous differential equations, Bull. Austr. Math. Soc. 34 (1986), 253265.
5. K. C. Chang and L. Sanchez, Nontrivial periodic solutions of a nonlinear beam equation, Math. Meth. in the Appl. Sci. 4 (1982), 194205.
4. A. Bahri and L. Sanchez, Periodic solutions of a nonlinear telegraph equation, B.U.M.I. 18B (1981), 709720.
3. L. Sanchez, Periodic solutions of a nonlinear evolution equation with a linear dissipative term, Rend. Sem. Mat. Univ. Politecn. Torino, 37 (1980), 183191.
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), 305307.
1. L. Sanchez, A note on a differential equation of the dynamics of wires, B.U.M.I. 16A, (1979), 391397.
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 FisherKolmogorov  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 twopoint 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 nonautonomous 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 nonautonomous systems, Views on ODEs, Univ. Aveiro, Junho 2006.
7. On bounded trajectories for some nonautonomous Systems, 1st Iberian mathematical meeting, Lisboa, Fevereiro 2007.
8.Heteroclinics for some nonautonomous second order differential equations, Nonlinear Differential Equations – A tribute to the work of Patrick Habets & Jean Mawhin, Brussels September 2008.
9. Heteroclinics for some nonautonomous 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 ISTIME, 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 reactiondiffusion, International Conference on Differential & Difference Equations and Applications, Ponta Delgada, Julho 2011.
13. Travelling Waves and Critical Speed in Equations of FisherKolmogorov type, Intensive twomonth 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 twomonth 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 Jan1 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 minischool on Differential Equations held at the Mathematical Institute of the Czech Academy of Sciences, Brno branch, May 2013.