Quasilinear elliptic problems with multivalued terms

Czechoslovak Mathematical Journal

Volumn 50, Issue 4, 2000, Pages 803-823

  Halidias, Nikolaos ^a   Papageorgiou, Nikolaos S ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Critical point; Dirichlet problem; Mountain Pass Theorem; Multivalued term; Neumann problem; p Laplacian; Palais Smale condition; Rayleigh quotient; Saddle Point Theorem; Subdifferential

Indexed keywords

EID: 0035648860     PISSN: 00114642     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022416729213     Document Type: Article

References (23)

1. R. Adams: Sobolev Spaces. Academic Press, New York, 1975.
2. W. F. Ames: Nonlinear Partial Differential Equations in Engineering. Academic Press, New York, 1965.
3. A. Ambrosetti and P. H. Rabinowitz: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14 (1973), 349-381.
4. A. Anane and J. P. Gossez: Strongly nonlinear elliptic problems near resonance: a variational approach. Comm. Partial Differential Equations 15 (1990), 1141-1159.
5. D. Arcoya and M. Calahorrano: Some discontinuous problems with a quasilinear operator. J. Math. Anal. Appl. 187 (1994), 1059-1072.
6. L. Boccardo, P. Drábek, D. Giachetti and M. Kučera: Generalization of Fredholm alternative for nonlinear differential operators. Nonlinear Anal. TMA 10 (1986), 1083-1103.
7. K. C. Chang: Variational methods for nondifferentiable functionals and their applications to partial differential equations. J. Math. Anal. Appl. 80 (1981), 102-129.
8. D. Costa and C. Magalhaes: Existence results for perturbations of the p-Laplacian. Nonlinear Anal. TMA 24 (1995), 409-418.
9. C. De Coster: Pairs of positive solutions for the one-dimensional p-Laplacian. Nonlinear Anal. TMA 23 (1994), 669-681.
10. p-2u′)′+f(t, u) = 0, u(0) = u(T) = 0, p > 1. J. Differential Equations 80 (1989), 1-13.
11. A. Friedman: Generalized heat transfer between solids and gases under nonlinear boundary conditions. J. Math. Mech. 8 (1959), 161-184.
12. Z. Guo: Boundary value problems for a class of quasilinear ordinary differential equations. Differential Integral Equations 6 (1993), 705-719.
13. A. El. Hachimi, J.-P. Gossez: A note on a nonresonance condition for a quasilinear elliptic problem. Nonlinear Anal. TMA 22 (1994), 229-236.
14. S. Hu and N. S. Papageorgiou: Handbook of Multivalued Analysis Volume I: Theory. Kluwer Academic Publishers, Dordrecht, 1997.
15. A. Ioffe and V. Tichomirov: Theory of Extremal Problems. North Holland, Amsterdam, 1979.
16. N. Kenmochi: Pseudomonotone operators and nonlinear elliptic boundary value problems. J. Math. Soc. Japan 27 (1975), 121-149.
17. A. Kufner, O. John and S. Fučík: Function Spaces. Noordhoff, Leyden, The Netherlands, 1977.
18. p-2x = 0. Proc. AMS. vol. 109, 1991, pp. 157-164.
19. P. H. Rabinowitz: Some minimax theorems and applications to nonlinear partial differential equations. Nonlinear Analysis: A collection of papers of E. Rothe (L. Cesari, R. Kannan, H. F. Weinberger, eds.). Acad. Press, New York, 1978, pp. 161-177.
20. P. H. Rabinowitz: Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS, Regional Conference Series in Math, No 65, AMS, Providence, R. J., 1986.
21. R. Showalter: Monotone Operators in Banach Space and Nonlinear Partial Differential Equations. Math. Surveys, vol. 49, AMS, Providence, R. I., 1997.
22. A. Szulkin: Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems. Ann. Inst. H. Poincare Anal. Non Linéaire 3 (1986) 77-109.
23. E. Zeidler: Nonlinear Functional Analysis and its Applications II. Springer Verlag, New York, 1990.