Existence of ground states for fractional Kirchhoff equations with general potentials via Nehari-Pohozaev manifold
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)...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2018-07-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/142/abstr.html |
| Summary: | 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]. |
|---|---|
| ISSN: | 1072-6691 |