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  • Nonhomogeneous Dirichlet problems without the Ambrosetti-Rabinowitz condition
    Li, Gang, matematik ...
    We consider the existence of solutions of the following ▫$p(x)$▫-Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition: ▫$$ \begin{cases} -\text{div} \, (|\nabla u|^{p(x)-2}\nabla ... u) = f(x,u) & \text{ in } \quad \Omega , \\ u=0 & \text{ on } \quad \partial \Omega . \end{cases} $$▫ We give a new growth condition and we point out its importance for checking the Cerami compactness condition. We prove the existence of solutions of the above problem via the critical point theory, and also provide some multiplicity properties. The present paper extend previous results of Q. Zhang and C. Zhao (Existence of strong solutions of a ▫$p(x)$▫-Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition, Computers and Mathematics with Applications, 2015) and we establish the existence of solutions under weaker hypotheses on the nonlinear term.
    Source: Topological Methods in Nonlinear Analysis. - ISSN 1230-3429 (Vol. 51, no. 1, March 2018, str. 55-77)
    Type of material - article, component part ; adult, serious
    Publish date - 2018
    Language - english
    COBISS.SI-ID - 18162521

    Link(s):

    http://dx.doi.org/10.12775/TMNA.2017.037
    Repository of the University of Ljubljana – RUL
    DOI

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