Strongly nonlinear second order differential inclusions with generalized boundary conditions

Journal of Mathematical Analysis and Applications

Volumn 287, Issue 2, 2003, Pages 348-364

  Kourogenis, Nikolaos C ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Continuous selection; Differential inclusion; Dirichlet problem; Fixed point problem; Maximal monotone map; Measurable selection; Multivalued Leray Schauder alternative theorem; Nagumo Hartman condition; Neumann problem; P Laplacian; Periodic problem; Resolvent operator; Usc and lsc multifunction; Yosida approximation

Indexed keywords

EID: 0346269031     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00511-5     Document Type: Article

References (34)

1. R. Bader, A topological fixed point index theory for evolution inclusions, preprint, University of Munich (1999).
2. L. Boccardo, P. Drabek, D. Giachetti, M. Kučera, Generalization of Fredholm alternative for nonlinear differential operators, Nonlinear Anal. 10 (1986) 1083-1103.
3. H. Brezis, Opérateurs Maximaux Monotones, North-Holland, Amsterdam, 1973.
4. H. Dang, S.F. Oppenheimer, Existence and uniqueness results for some nonlinear boundary value problems, J. Math. Anal. Appl. 198 (1996) 35-48.
5. K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
6. p-2u′)′ + f(t, u) = 0, u(0) = u(b) = 0, J. Differential Equations 80 (1989) 1-13.
7. M. Del Pino, M. Elgueta, A. Murua, Existence and multiplicity of solutions with prescribed period for a second order quasilinear ode, Nonlinear Anal. 18 (1992) 79-92.
8. J. Dugundji, A. Granas, Fixed Point Theory, in: Monografie Matematyczne, Vol. 61, Polish Scientific, Warsaw, 1982.
9. L. Erbe, W. Krawcewicz, Nonlinear boundary value problems for differential inclusions y″ ∈ (t, y, y′), Ann. Polon. Math. 54 (1991) 195-226.
10. L. Erbe, W. Krawcewicz, Boundary value problems for second order nonlinear differential inclusions, in: Lecture Notes in Pure and Applied Math., Vol. 127, Marcel Dekker, New York, 1991, pp. 115-135.
11. L. Erbe, W. Krawcewicz, Existence of solutions to boundary value problems for impulsive second order differential inclusions, Rocky Mountain J. Math. 22 (1992) 1-20.
12. L. Erbe, W. Krawcewicz, S. Chen, Some existence results for solutions of differential inclusions with retardation, Ann. Polon. Math. 54 (1991) 227-239.
13. L. Erbe, W. Krawcewicz, G. Peschke, Bifurcation of a parametrized family of boundary value problems for second order differential inclusions, Ann. Mat. Pura Appl. 166 (1993) 169-195.
14. C. Fabry, D. Fayyad, Periodic solutions of second order differential equations with a p-Laplacian and asymmetric nonlinearities, Rend. Istit. Mat. Univ. Trieste 24 (1992) 207-227.
15. M. Frigon, Application de la theorie de la transversalite topologique a des problemes non lineaires pour des equations differentielles ordinaires, Dissertationes Math. 269 (1999).
16. M. Frigon, Theoremes d'existence des solutions d'inclusions differentielles, in: Topological Methods in Differential Equations and Inclusions, in: NATO ASI Set. C, Vol. 472, Kluwer, Dordrecht, 1995, pp. 51-87.
17. M. Frigon, A. Granas, Problemes aux limites pour des inclusions defferentielles de type semi-continues inferieurement, Riv. Mat. Univ. Parma 17 (1991) 87-97.
18. Z. Guo, Boundary value problems of a class of quasilinear differential equations, Differential Integral Equations 6 (1993) 705-719.
19. P. Halmos, Finite Dimensional Vector Spaces, Springer, Berlin, 1974.
20. N, J. Differential Equations 147 (1998) 123-154.
21. N. Halidias, N.S. Papageorgiou, Existence of solutions for quasilinear second order differential inclusions with nonlinear boundary conditions, J. Comput. Appl. Math. 113 (2000) 51-64.
22. P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964.
23. E. Hewitt, K. Stromberg, Real and Abstract Analysis, Springer, New York, 1975.
24. S. Hu, N.S. Papageorgiou, Handbook of Multivalued Analysis. Volume I: Theory, Kluwer, Dordrecht, 1997.
25. S. Hu, N.S. Papageorgiou, Handbook of Multivalued Analysis. Volume II: Applications, Kluwer, Dordrecht, 2000.
26. D. Kandilakis, N.S. Papageorgiou, Existence theorems for nonlinear boundary value problems for second order differential inclusions, J. Differential Equations 132 (1996) 107-125.
27. D. Kandilakis, N.S. Papageorgiou, Neumann problem for a class of quasilinear differential equations, Atti Sem. Mat. Fis. Univ. Modena 48 (1999) 1-15.
28. N.C. Kourogenis, N.S. Papageorgiou, On a class of quasilinear differential equations: the Neumann problem, Methods Appl. Anal. 5 (1999) 273-282.
29. S. Kyritsi, N. Matzakos, N.S. Papageorgiou, Periodic problems for strongly nonlinear second order differential inclusions, J. Differential Equations 183 (2002) 279-302.
30. R. Manasevich, J. Mawhin, Periodic solutions for nonlinear systems with p-Laplacian-like operators, J. Differential Equations 145 (1998) 367-393.
31. M. Marcus, V. Mizel, Absolute continuity on tracks and mappings of Sobolev spaces, Arch. Rational Mech. Anal. 45 (1972) 294-320.
32. T. Pruszko, Topological degree methods in multivalued boundary value problems, Nonlinear Anal. 9 (1981) 959-973.
33. T. Pruszko, Some applications of the topological degree theory to multivalued boundary value problems, Dissertationes Math. 229 (1984).
34. E. Zeidler, Nonlinear Functional Analysis and Its Applications II, Springer, New York, 1990.