Shi, H., Chen, H. (2017). Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth. Bulletin of the Iranian Mathematical Society, 43(1), 147-161.

H. Shi; H. Chen. "Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth". Bulletin of the Iranian Mathematical Society, 43, 1, 2017, 147-161.

Shi, H., Chen, H. (2017). 'Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth', Bulletin of the Iranian Mathematical Society, 43(1), pp. 147-161.

Shi, H., Chen, H. Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth. Bulletin of the Iranian Mathematical Society, 2017; 43(1): 147-161.

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

^{}School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P. R. China.

Receive Date: 08 May 2015,
Revise Date: 10 September 2015,
Accept Date: 22 October 2015

Abstract

In this paper, we consider the following Kirchhoff-type equations: $-\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)\Delta u+V(x) u=\lambda$ $f(x,u)+u^{5}, \quad \mbox{in }\mathbb{R}^{3},$ $u(x)>0, \quad \mbox{in }\mathbb{R}^{3},$ $u\in H^{1}(\mathbb{R}^{3}) ,$ 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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