Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking

We consider the Dirichlet problem for the equation −∆u = λu + h(x)f(u) , with h changing sign. In particular, we study existence of nontrivial solutions in the case where f has superlinear growth, but is not assumed to be odd. Two different approaches are used: one involving Morse theory and one using min-max methods. Résumé Nous étudions le problème de Dirichlet pour l’équation −∆u = λu + h(x)f(u) , où h est une fonction qui …