Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking
- 1 February 1996
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Vol. 13 (1) , 95-115
- https://doi.org/10.1016/s0294-1449(16)30098-1
Abstract
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 change de signe. En particulier, nous établissons l’existence de solutions non triviales quand f est surlinéaire, mais pas nécessairement impair. Nous nous servons de deux approches différentes, l’une basée sur la théorie de Morse, et l’autre sur les méthodes d’enlacement.This publication has 7 references indexed in Scilit:
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