Abstract
In this paper, we study the existence of positive ground state solutions for non-autonomous Kirchhoff type problems: $$ -\Big (1+b\int _{\mathbb R^3} |\nabla u|^2\Big ) \Delta u+u=a(x)|u|^{p-1}u \quad \mbox {in } \mathbb {R}^3, $$ where $b>0$, $3\lt p\lt 5$ and $a:\mathbb R^3\rightarrow \mathbb R$ is such that $$ \lim _{|x|\rightarrow \infty } a(x)=a_\infty >0, $$ but no symmetry property on $a(x)$ is required.
Citation
Qilin Xie. Shiwang Ma. "Positive ground state solutions for some non-autonomous Kirchhoff type problems." Rocky Mountain J. Math. 47 (1) 329 - 350, 2017. https://doi.org/10.1216/RMJ-2017-47-1-329
Information