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Multiple solutions for nonlinear discontinuous elliptic problems near resonance

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Kourogenis N. C., Papageorgiou N. S.

Colloquium Mathematicum

1999

tom 81

nr 1

89-99

We consider a quasilinear elliptic eigenvalue problem with a discontinuous right hand side. To be able to have an existence theory, we pass to a multivalued problem (elliptic inclusion). Using a variational approach based on the critical point theory for locally Lipschitz functions, we show that we have at least three nontrivial solutions when $λ → λ_1$ from the left, $λ_1$ being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Kourogenis N. C.

1 Papageorgiou N. S.

1 1999

Wyniki wyszukiwania

Multiple solutions for nonlinear discontinuous elliptic problems near resonance