Geodesic
Multiple solutions for nonlinear discontinuous elliptic problems near resonance
Colloquium Mathematicum, Tome 81 (1999) no. 1, pp. 89-99 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm-81-1-89-99
Keywords: discontinuous function, generalized directional derivative, critical point, coercive functional, multiple solutions, Clarke subdifferential, Rayleigh quotient, first eigenvalue, p-Laplacian, elliptic inclusion, nonsmooth Palais-Smale condition

Nikolaos Kourogenis 1 ; Nikolaos Papageorgiou 1

1 
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Nikolaos Kourogenis; Nikolaos Papageorgiou. Multiple solutions for nonlinear discontinuous elliptic problems near resonance. Colloquium Mathematicum, Tome 81 (1999) no. 1, pp. 89-99. doi: 10.4064/cm-81-1-89-99

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