Existence and multiplicity of solutions for nonlinear periodic problems with the scalar p-Laplacian and double resonance

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Papageorgiou, Evgenia H.¹  Papageorgiou, Nikolaos S.² 

[1] Hellen Naval Acad, Dept Math, Piraeus 45110, Greece

[2] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

关键词: Spectrum of the scalar p-Laplacian;    Double resonance;    Critical groups reduced homology sequence;    Morse theory;    Existence and multiplicity theorems;   

DOI  :  10.1016/j.jde.2013.07.053

来源: Elsevier

【 摘 要 】

We consider nonlinear periodic problems driven by the scalar p-Laplacian and with a Caratheodory reaction which can exhibit double resonance at +/-infinity. Combining variational methods based on the critical point theory with Morse theoretic techniques, we show that we have existence when the double resonance occurs at any spectral interval and we have multiplicity with at least three nontrivial solutions, when the double resonance occurs at any spectral interval distinct from the principal one [(lambda) over cap (0) = 0, (lambda) over cap (1)]. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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