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  • Nonlinear Dirichlet problems with double resonance
    Aizicovici, Sergiu, 1948- ; Papageorgiou, Nikolaos, 1958- ; Staicu, Vasile, 1960-
    We study a nonlinear Dirichlet problem driven by the sum of a ▫$p$▫-Laplacian (▫$p>2$▫) and a Laplacian and which at ▫$\pm\infty$▫ is resonant with respect to the spectrum of ▫$\left( ... -\Delta_{p},W_{0}^{1,p}\left( \Omega \right) \right) $▫ and at zero is resonant with respect to the spectrum of ▫$\left( -\Delta,H_{0}^{1}\left( \Omega \right) \right) $▫ (double resonance). We prove two multiplicity theorems providing three and four nontrivial solutions respectivelly, all with sign information. Our approach uses critical point theory together with truncation and comparison techniques and Morse theory.
    Source: Communications on pure and applied analysis. - ISSN 1534-0392 (Vol. 16, no. 4, 2017, str. 1147-1168)
    Type of material - article, component part ; adult, serious
    Publish date - 2017
    Language - english
    COBISS.SI-ID - 18011481

    Link(s):

    http://aimsciences.org/journals/doIpChk.jsp?paperID=13910&mode=full
    http://doi.org/10.3934/cpaa.2017056
    DOI

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