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  • Multiplicity results for a nonlinear Robin problem with variable exponent
    Saiedinezhad, Somayeh ; Rǎdulescu, Vicenţiu, 1958-
    The nonlinear weighted Robin problem ▫$$\begin{cases} -\text{div}(a(x)|\nabla u|^{p(x)-2}\nabla u) + b(x)|u|^{q(x)-2}\\\hspace{3cm} - \lambda c(x)|u|^{r(v)-2} u(x) = f(x,u); & \text{in} \quad \Omega, ... \\ |\nabla u|^{p(x)-2} \frac{\partial u}{\partial \nu} + \beta(x)|\nabla u|^{p(x)-2}u = 0 & \text{on} \quad \partial\Omega \end{cases}$$▫ is studied in the present paper. We are concerned with maximum or minimum growth of the corresponding energy functional by various conditions on ▫$p$▫, ▫$q$▫, ▫$r$▫. We also obtain qualitative properties about the bahavior of energy functional and, by applying some variational methods, several existence results for tha sequence of weak solutiond are deduced. Finally, we study our problem by modeling as a nonlinear eigenvalue problem.
    Source: Journal of nonlinear and convex analysis. - ISSN 1345-4773 (Vol. 17, no. 8, 2016, str. 1567-1582)
    Type of material - article, component part ; adult, serious
    Publish date - 2016
    Language - english
    COBISS.SI-ID - 17792089

    Link(s):

    http://www.ybook.co.jp/online2/opjnca/vol17/p1567.html

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