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On some asymmetric elliptic problems with indefinite weights. (Sur certains problèmes elliptiques asymétriques avec poids indéfinis.) (French. English summary) Zbl 0973.35147
Summary: We prove the existence of a first nontrivial eigenvalue for the problem $-\Delta_p u= \lambda[m(x)(u^+)^{p- 1}- n(x)(u^-)^{p- 1}]\quad\text{in }\Omega,\quad u=0\quad\text{on }\partial\Omega.$ As applications we study the solvability of $-\Delta_p u= f(x, u)\quad\text{in }\Omega,\quad u= 0\quad\text{on }\partial\Omega$ as well as the Fučik spectrum with weights for the $$p$$-Laplacian.

MSC:
 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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