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Publicly Available Published by De Gruyter March 10, 2016

A Resonant-Superlinear Elliptic Problem Revisited

Mabel Cuesta and Colette De Coster

Abstract

We consider the resonant-superlinear elliptic problem -Δu = λ1u + (u+)q + f (x), with Dirichlet boundary conditions on a bounded regular domain of ℝN. We assume that with s > N satisfies ∫Ω1 < 0 and (λ1, φ1) is the first eigenpair of −Δ on H10(Ω). We apply a non-well ordered lower and upper solution result on a family of modified problems and obtain a sequence of localized solutions of these modified problems. Thanks to this localization and a precise bootstrap argument we are abble to prove that for large modification, these solutions are, in fact, solutions of our initial problem. The problem was already considered in [2] by a totally different approach.

Published Online: 2016-03-10
Published in Print: 2013-02-01

© 2016 by Advanced Nonlinear Studies, Inc.

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