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  • Nonlinear nonhomogeneous Dirichlet equations involving a superlinear nonlinearity
    Papageorgiou, Nikolaos, 1958- ; Winkert, Patrick, 1981-
    We consider a nonlinear elliptic Dirichlet equation driven by a nonlinear nonhomogeneous differential operator involving a Carathéodory function which is ▫$(p)$▫-superlinear but does not satisfy the ... Ambrosetti-Rabinowitz condition. First we prove a three-solutions-theorem extending an earlier classical result of Z. Q. Wang [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 8, No. 1, 43-57 (1991)]. Subsequently, by imposing additional conditions on the nonlinearity ▫$f(x,\cdot)$▫, we produce two more nontrivial constant sign solutions and a nodal solution for a total of five nontrivial solutions. In the special case of ▫$(p,2)$▫-equations we prove the existence of a second nodal solution for a total of six nontrivial solutions given with complete sign information. Finally, we study a nonlinear eigenvalue problem and we show that the problem has at least two nontrivial positive solutions for all parameters ▫$\lambda > 0$▫ sufficiently small where one solution vanishes in the Sobolev norm as ▫$\lambda \to 0^+$▫ and the other one blows up (again in the Sobolev norm) as ▫$\lambda \to 0^+$▫.
    Vir: Results in mathematics = Resultate der Mathematik. - ISSN 1422-6383 (Vol. 70, iss. 1, 2016, str. 31-79)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2016
    Jezik - angleški
    COBISS.SI-ID - 17824089

    Povezava(-e):

    http://dx.doi.org/10.1007/s00025-015-0461-3

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