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  • Positive solutions for the Neumann ▫$p$▫-Laplacian with superdiffusive reaction
    Gasiński, Leszek ; Papageorgiou, Nikolaos, 1958-
    We consider a generalized logistic equation driven by the Neumann ▫$p$▫-Laplacian and with a reaction that exhibits a superdiffusive kind of behavior. Using variational methods based on the critical ... point theory, together with truncation and comparison techniques, we show that there exists a critical value ▫$\lambda_\ast > 0$▫ of the parameter, such that if ▫$\lambda > \lambda_\ast$▫, the problem has at least two positive solutions, if ▫$\lambda = \lambda_\ast$▫, the problem has at least one positive solution and it has no positive solution if ▫$\lambda \in (0, \lambda_\ast)$▫. Finally, we show that for all ▫$\lambda \geqslant \lambda_\ast$▫, the problem has a smallest positive solution.
    Source: Bulletin of the Malaysian Mathematical Sciences Society. - ISSN 0126-6705 (Vol. 40, iss. 4, Oct. 2017, str. 1711-1731)
    Type of material - article, component part ; adult, serious
    Publish date - 2017
    Language - english
    COBISS.SI-ID - 18077017

    Link(s):

    http://doi.org/10.1007/s40840-015-0212-3
    DOI

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