We prove the existence of a nontrivial solution for a nonlinear elliptic problem -Δu = μu + a(x)g(u) with Dirichlet boundary condition on a bounded domain, where g is superlinear both at zero and at infinity, and where a(x) changes sign and μ > 0.
Ramos, M., Terracini, S., Troestler, C. (1997). Superlinear elliptic problems with sign changing nonlinearity [Problèmes elliptiques sur-linéaires avec non-linéarité sans signe défini]. COMPTES RENDUS DE L'ACADÉMIE DES SCIENCES. SÉRIE 1, MATHÉMATIQUE, 325(3), 283-286 [10.1016/S0764-4442(97)83956-0].
Superlinear elliptic problems with sign changing nonlinearity [Problèmes elliptiques sur-linéaires avec non-linéarité sans signe défini]
TERRACINI, SUSANNA;
1997
Abstract
We prove the existence of a nontrivial solution for a nonlinear elliptic problem -Δu = μu + a(x)g(u) with Dirichlet boundary condition on a bounded domain, where g is superlinear both at zero and at infinity, and where a(x) changes sign and μ > 0.
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