positive solutions for asymptotically periodic kirchhoff-type equations with critical growth

نویسندگان

h. shi

school of mathematics and statistics‎, ‎central south university‎, ‎changsha‎, ‎410083 hunan‎, ‎p‎. ‎r‎. ‎china. h. chen

school of mathematics and statistics‎, ‎central south university‎, ‎changsha‎, ‎410083 hunan‎, ‎p‎. ‎r‎. ‎china.

چکیده

in this paper‎, ‎we consider the following kirchhoff-type equations‎: ‎$-‎left(a+bint_{mathbb{r}^{3}}|nabla u|^{2}right)delta u+v(x) u=lambda$ $f(x,u)+u^{5}‎, ‎quad mbox{in }mathbb{r}^{3},$ ‎$u(x)>0‎, ‎quad mbox{in }mathbb{r}^{3},$ ‎$uin h^{1}(mathbb{r}^{3})‎ ,‎$ ‎ ‎‎‎where $a,b>0$ are constants and $lambda$ is a positive parameter‎. ‎the aim of this paper is to study the existence of positive solutions for kirchhoff-type equations with a nonlinearity in the critical growth under some suitable assumptions on $v(x)$ and $f(x,u)$‎. ‎recent results from the literature are improved and extended.

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Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth

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bulletin of the iranian mathematical society

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