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  • Singular and superlinear perturbations of the eigenvalue problem for the Dirichlet ▫$p$▫-Laplacian
    Papageorgiou, Nikolaos, 1958- ; Zhang, Chao, 1981-
    We consider a nonlinear Dirichlet problem, driven by the ▫$p$▫-Laplacian with a reaction involving two parameters ▫$\lambda \in {\mathbb {R}}, \theta >0$▫. We view the problem as a perturbation of ... the classical eigenvalue problem for the Dirichlet problem. The perturbation consists of a parametric singular term and of a superlinear term. We prove a nonexistence and a multiplicity results in terms of the principal eigenvalue ▫${\hat{\lambda }}_1>0$▫ of ▫$(-\Delta _p, W_0^{1,p}(\Omega ))$▫. So, we show that if ▫$\lambda \ge {\hat{\lambda }}_1$▫ and ▫$\theta>0$▫, then the problem has no positive solution, while if ▫$\lambda <{\hat{\lambda }}_1$▫ and ▫$\theta >0$▫ is suitably small (depending on ▫$\lambda$▫), there are two positive smooth solutions.
    Source: Results in mathematics = Resultate der Mathematik. - ISSN 1422-6383 (Vol. 76, iss. 1, March 2021, art. 28 (18 str.))
    Type of material - article, component part ; adult, serious
    Publish date - 2021
    Language - english
    COBISS.SI-ID - 46885379

    Link(s):

    https://link.springer.com/content/pdf/10.1007/s00025-020-01340-y.pdf
    DOI

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