Nehari-type ground state solutions for asymptotically periodic fractional Kirchhoff-type problems in RN$\mathbb{R}^{N}$
Nehari-type ground state solutions for asymptotically periodic fractional Kirchhoff-type problems in RN$\mathbb{R}^{N}$
In this paper, we studied the following fractional Kirchhoff-type equation: $$\biggl(a+b \int_{\mathbb{R}^{N}} \bigl\vert (-\triangle)^{\frac{\alpha }{2}}u \bigr\vert ^{2}\,\mathrm{d}x \biggr) (-\triangle)^{\alpha }u+V(x)u=f(x,u), \quad x\in{\mathbb{R}}^{N}, $$ where a, b are positive constants, $\alpha\in(0,1)$ , $N\in (2\alpha,4\alpha)$ , $(-\triangle)^{\alpha}$ is the fractional Laplacian operator, $V(x)$ and $f(x,u)$ are periodic or asymptotically periodic in x. …