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Colloquium Mathematicum

1998 | 78 | 2 | 213-223
Tytuł artykułu

Discontinuous quasilinear elliptic problems at resonance

Autorzy
Treść / Zawartość
Warianty tytułu
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
Czasopismo
Rocznik
Tom
Numer
Strony
213-223
Opis fizyczny
Daty
wydano
1998
otrzymano
1998-01-28
poprawiono
1998-03-16
Twórcy
• Department of Mathematics National Technical University Zografou Campus Athens 157 80, Greece
• 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.
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Bibliografia
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