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  • Nodal and multiple solutions for nonlinear elliptic equations involving a reaction with zeros
    Gasiński, Leszek ; Papageorgiou, Nikolaos, 1958-
    We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a Carathéodory reaction. Imposing control on the growth of the reaction only near zero and assuming ... that it has two constant sign ▫$z$▫-dependent zeros, we prove two multiplicity theorem producing three nontrivial smooth solutions, one positive, the second negative and the third nodal. Then for the particular case of ▫$(p,2)$▫-equations and assuming that the reaction is ▫$(p-1)$▫-superlinear near ▫$\pm \infty$▫, without satisfying the Ambrosetti-Rabinowitz condition, we show that the problem has at least six nontrivial smooth solutions.
    Source: Dynamics of partial differential equations. - ISSN 1548-159X (Vol. 12, no. 1, 2015, str. 13-42)
    Type of material - article, component part ; adult, serious
    Publish date - 2015
    Language - english
    COBISS.SI-ID - 18195545

    Link(s):

    http://doi.org/10.4310/DPDE.2015.v12.n1.a2
    DOI

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