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- W3017032477 abstract "In this article using Nehari manifold method we study the multiplicity of solutions of the following nonlocal elliptic system involving variable exponents and concave-convex nonlinearities: begin{equation*} ;;; begin{array}{rl} (-Delta)_{p(cdot)}^{s} u&=lambda~ a(x)| u|^{q(x)-2}u+frac{alpha(x)}{alpha(x)+beta(x)}c(x)| u|^{alpha(x)-2}u| v| ^{beta(x)},hspace{2mm} xin Omega; (-Delta)_{p(cdot)}^{s} v&=mu~ b(x)| v|^{q(x)-2}v+frac{alpha(x)}{alpha(x)+beta(x)}c(x)| v|^{alpha(x)-2}v| u| ^{beta(x)},hspace{2.5mm} xin Omega; u=v&=0 ,hspace{1cm} xin Omega^c:=mathbb R^NsetminusOmega, end{array} end{equation*} where $Omegasubsetmathbb R^N,~Ngeq2$ is a smooth bounded domain, $lambda,mu>0$ are the parameters, $sin(0,1),$ $pin C(mathbb R^Ntimes mathbb R^N,(1,infty))$ and $q,alpha,betain C(overline{Omega},(1,infty))$ are the variable exponents and $a,b,cin C(overline{Omega},[0,infty))$ are the non-negative weight functions. We show that there exists $Lambda>0$ such that for all $lambda+mu<Lambda$, there exist two non-trivial and non-negative solutions of the above problem under some assumptions on $q,alpha,beta$." @default.
- W3017032477 created "2020-04-24" @default.
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- W3017032477 date "2020-04-20" @default.
- W3017032477 modified "2023-09-27" @default.
- W3017032477 title "Nehari manifold for fractional p(.)-Laplacian system involving concave-convex nonlinearities" @default.
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