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Journal Articles Advanced Nonlinear Studies Year : 2013

A Resonant-Superlinear Elliptic Problem Revisited

Abstract

We consider the resonant-superlinear elliptic problem−∆u=λ1u+(u+)q+f(x), withDirichlet boundary conditions on a bounded regular domain ofRN. We assume that 1Nsatisfies∫Ωfφ1<0 and (λ1,φ1) is the first eigenpair of−∆onH10(Ω). We apply a non-well ordered lower and upper solution result on a family ofmodified 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 forlarge modification, these solutions are, in fact, solutions of our initial problem.The problem was already considered in [2] by a totally different approach.
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Dates and versions

hal-03137546 , version 1 (10-02-2021)

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Mabel Cuesta, Colette De Coster. A Resonant-Superlinear Elliptic Problem Revisited. Advanced Nonlinear Studies, 2013, 13 (1), pp.97-114. ⟨10.1515/ans-2013-0106⟩. ⟨hal-03137546⟩
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