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  • Multiple solutions for nonlinear nonhomogeneous resonant coercive problems
    Averna, Diego ; Papageorgiou, Nikolaos, 1958- ; Tornatore, Elisabetta
    We consider a nonlinear, nonhomogeneous Dirichlet problem driven by the sum of a ▫$p$▫-Laplacian ▫$(2<p)$▫ and a Laplacian. The reaction term is a Carathéodory function ▫$f(z,x)$▫ which is resonant ... with respect to the principal eigenvalue of ▫$(-\Delta_p,W^{1,p}_0(\Omega))$▫. Using variational methods combined with truncation and comparison techniques and Morse theory (critical groups) we prove the existence of three nontrivial smooth solutions all with sign information and under three different conditions concerning the behavior of ▫$f(z, \cdot)$▫ near zero. By strengthening the regularity of ▫$f(z, \cdot)$▫, we are able to generate a second nodal solution for a total of four nontrivial smooth solutions.
    Vir: Discrete and continuous dynamical systems. Series S. - ISSN 1937-1632 (Vol. 11, iss. 2, Apr. 2018, str. 155-178)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2018
    Jezik - angleški
    COBISS.SI-ID - 18161497

    Povezava(-e):

    http://dx.doi.org/10.3934/dcdss.2018010
    DOI

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