Existence of ground states for fractional Kirchhoff equations with general potentials via Nehari-Pohozaev manifold

• Main Authors: Jing Chen, Xianhua Tang, Sitong Chen
• Format: Article
• Language: English
• Published: Texas State University 2018-07-01
• Series: Electronic Journal of Differential Equations
• Subjects: Fractional Kirchhoff equation; Nehari-Pohozaev manifold; ground state solutions
• Online Access: http://ejde.math.txstate.edu/Volumes/2018/142/abstr.html

We consider the nonlinear fractional Kirchhoff equation $$ \Big(a+b\int_{\mathbb R^3}|(-\Delta)^{\alpha/2} u|^2\,\mathrm{d}x\Big) (-\Delta)^\alpha u+V(x)u=f(u) \quad \text{in } \mathbb R^3, u\in H^{\alpha}(\mathbb R^3), $$ where a>0, $b\ge 0$, $\alpha\in(3/4, 1)$ are three constants, V(x) is differentiable and $f\in C^1(\mathbb R, \mathbb R)$. Our main results show the existence of ground state solutions of Nehari-Pohozaev type, and the existence of the least energy solutions to the above problem with general superlinear and subcritical nonlinearity. These results are proved by applying variational methods and some techniques from [27].