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  • Pairs of positive solutions for ▫$p$▫-Laplacian equations with sublinear and superlinear nonlinearities which do not satisfy the AR-condition
    Papageorgiou, Nikolaos, 1958- ; Rocha, Eugénio M.
    We consider a nonlinear Dirichlet problem driven by the ▫$p$▫-Laplacian differential. The right-hand-side nonlinearity, exhibits a ▫$(p - 1)$▫-sublinear term of the form ▫$m(z)|x|^{r - 2}x, r<p$▫ ... (concave term), and a Carathéodory term ▫$f(z,x)$▫ which is ▫$(p - 1)$▫-superlinear near ▫$+\infty $▫. However, it does not satisfy the usual Ambrosetti-Rabinowitz condition (AR-condition). Instead we employ a more general condition. Using a variational approach based on the critical point theory and the Ekeland variational principle, we show the existence of two nontrivial positive smooth solutions and then the existence of two nontrivial negative smooth solutions.
    Vir: Nonlinear Analysis. Theory, Methods and Applications. - ISSN 0362-546X (Vol. 70, iss. 11, 2009, str. 3854-3863)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2009
    Jezik - angleški
    COBISS.SI-ID - 18067033

    Povezava(-e):

    http://dx.doi.org/10.1016/j.na.2008.07.042
    DOI

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