Discontinuous quasilinear elliptic problems at resonance

• Autorzy: Nikolaos C. Kourogenis , Nikolaos S. Papageorgiou
• Języki publikacji: EN

Abstrakty

EN

In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.

Słowa kluczowe

EN

compact embedding; Poincaré's inequality; Palais-Smale condition; critical point; variational method; Mountain Pass Theorem; subdifferential; problems at resonance; locally Lipschitz functional

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 78
• Numer: 2
• Strony: 213-223

Daty

wydano

1998

otrzymano

1998-01-28

poprawiono

1998-03-16

Twórcy

autor

Nikolaos C. Kourogenis

• Department of Mathematics National Technical University Zografou Campus Athens 157 80, Greece

autor

Nikolaos S. Papageorgiou

• Department of Mathematics, National Technical University, Zografou Campus, Athens 157 80, Greece

Bibliografia

• [1] Ahmad, S., Lazer, A. and Paul, J., Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976), 933-944.
• [2] Ambrosetti, A. and Rabinowitz, P., Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381.
• [3] Benci, V., Bartolo, P. and Fortunato, D., Abstract critical point theorems and applications to nonlinear problems with strong resonance at infinity, Nonlinear Anal. 7 (1983), 961-1012.
• [4] Browder, F. and Hess, P., Nonlinear mappings of monotone type, J. Funct. Anal. 11 (1972), 251-294.
• [5] Chang, K. C., Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129.
• [6] Clarke, F. H., Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
• [7] Lazer, A. and Landesman, E., Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623.
• [8] Lindqvist, P., On the equation $\div(|Dx|^{p-2}Dx)+λ |x|^{p-2}x=0$, Proc. Amer. Math. Soc. 109 (1991), 157-164.
• [9] Rabinowitz, P. H., Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math. 65, Amer. Math. Soc., Providence, R.I., 1986.
• [10] Thews, K., Nontrivial solutions of elliptic equations at resonance, Proc. Roy. Soc. Edinburgh Sect. A 85 (1980), 119-129.
• [11] Ward, J., Applications of critical point theory to weakly nonlinear boundary value problems at resonance, Houston J. Math. 10 (1984), 291-305.