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Superlinear Indefinite Elliptic Problems and Pohoz′aev Type Identities

✍ Scribed by Miguel Ramos; Susanna Terracini; Christophe Troestler

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 436 KB
Volume: 159
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3332

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✦ Synopsis

We prove the existence of a nontrivial solution for a nonlinear elliptic problem &2u=+u+a(x) g(u) with Dirichlet boundary condition on a bounded domain, where g is superlinear both at zero and at infinity, a(x) changes sign and +>0.

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A Priori Bounds and Multiple Solutions for Superlinear Indefinite Elliptic Problems

✍ H. Amann; J. López-Gómez 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 528 KB

In this work we study existence and multiplicity questions for positive solutions of second-order semilinear elliptic boundary value problems, where the nonlinearity is multiplied by a weight function which is allowed to change sign and vanish on sets of positive measure. We do not impose a variatio