We establish existence and multiplicity theorems for a Dirichlet boundary-value problem at resonance. This problem is a nonlinear subcritical perturbation of a linear eigenvalue problem studied by Cuesta, and includes a sign-changing potential. We obtain solutions using the Mountain Pass lemma and the Saddle Point theorem. Our paper extends some recent results of Goncalves, Miyagaki, and Ma.
Submitted September 28, 2005. Published October 24, 2005.
Math Subject Classifications: 35A15, 35J60, 35P30, 58E05.
Key Words: Eigenvalue problem; semilinear elliptic equation; existence result; critical point.
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| Teodora-Liliana Dinu |
Department of Mathematics
"Fratii Buzesti" College
200352 Craiova, Romania
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