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  • Double resonance for Robin problems with indefinite and unbounded potential
    Papageorgiou, Nikolaos, 1958- ; Winkert, Patrick, 1981-
    We study a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential term. The nonlinearity ▫$f(x,s)$▫ is a Carathéodory function which is asymptotically linear as ... ▫$s \to \pm \infty$▫ and resonant. In fact we assume double resonance with respect to any nonprincipal, nonnegative spectral interval ▫$\left[ \hat{\lambda}_k, \hat{\lambda}_{k+1} \right]$▫. Applying variational tools along with suitable truncation and perturbation techniques as well as Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of constant sign.
    Source: Discrete and continuous dynamical systems. Series S. - ISSN 1937-1632 (Vol. 11, iss. 2, Apr. 2018, str. 323-344)
    Type of material - article, component part
    Publish date - 2018
    Language - english
    COBISS.SI-ID - 18160473

    Link(s):

    http://dx.doi.org/10.3934/dcdss.2018018
    DOI

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