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  • Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential
    Papageorgiou, Nikolaos, 1958- ; Rǎdulescu, Vicenţiu, 1958- ; Repovš, Dušan, 1954-
    We study perturbations of the eigenvalue problem for the negative Laplacian plus an indefinite and unbounded potential and Robin boundary condition. First we consider the case of a sublinear ... perturbation and then of a superlinear perturbation. For the first case we show that for ▫$\lambda < \widehat{\lambda}_{1}$▫ (▫$\widehat{\lambda}_{1}$▫ being the principal eigenvalue) there is one positive solution which is unique under additional conditions on the perturbation term. For ▫$\lambda \geq \widehat{\lambda}_{1}$▫ there are no positive solutions. In the superlinear case, for ▫$\lambda < \widehat{\lambda}_{1}$▫ we have at least two positive solutions and for ▫$\lambda \geq \widehat{\lambda}_{1}$▫ there are no positive solutions. For both cases we establish the existence of a minimal positive solution ▫$\bar{u}_{\lambda}$▫ and we investigate the properties of the map ▫$\lambda \mapsto \bar{u}_{\lambda}$▫.
    Vir: Discrete and continuous dynamical systems. - ISSN 1078-0947 (Vol. 37, no. 5, 2017, str. 2589-2618)
    Vrsta gradiva - članek, sestavni del
    Leto - 2017
    Jezik - angleški
    COBISS.SI-ID - 17925721

    Povezava(-e):

    http://dx.doi.org/10.3934/dcds.2017111
    Repozitorij Univerze v Ljubljani – RUL

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