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- W3089885685 abstract "In this paper, we consider a class of non-cooperative critical nonlocal equation system with variable exponents of the form: $$ left{ begin{array}{lll} -(-Delta)_{p(cdot,cdot)}^su - |u|^{p(x)-2}u = F_u(x,u,v) + |u|^{q(x)-2}u, quad &mbox{in},,mathbb{R}^N, (-Delta)_{p(cdot,cdot)}^sv + |v|^{p(x)-2}v = F_v(x,u,v) + |v|^{q(x)-2}u, quad &mbox{in},,mathbb{R}^N, u, v in W^{s,p(cdot,cdot)}(mathbb{R}^N), end{array}right. $$ where $nabla F = (F_u, F_v)$ is the gradient of a $C^1$-function $F: mathbb{R}^Ntimes mathbb{R}^2 rightarrow mathbb{R}^+$ with respect to the variable $(u, v) in mathbb{R}^2$. We also assume that${x in mathbb{R}^N: q(x) = p_s^ast(x)} neq emptyset$, here $p_s^ast(x)=Np(x,x)/(N-sp(x,x))$ is the critical Sobolev exponent for variable exponents. With the help of the Limit index theory and the concentration-compactness principles for fractional Sobolev spaces with variable exponents, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity." @default.
- W3089885685 created "2020-10-08" @default.
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- W3089885685 date "2020-08-07" @default.
- W3089885685 modified "2023-10-17" @default.
- W3089885685 title "Multiple solutions for a class of non-cooperative critical nonlocal equation system with variable exponents" @default.
- W3089885685 doi "https://doi.org/10.22541/au.159679628.82479833" @default.
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