solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看1287次
Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent. (arXiv:1710.03973v1 [math.AP])
来源于:arXiv
We prove the existence of ground state solutions by variational methods to
the nonlinear Choquard equations with a nonlinear perturbation \[ -{\Delta}u+
u=\big(I_\alpha*|u|^{\frac{\alpha}{N}+1}\big)|u|^{\frac{\alpha}{N}-1}u+f(x,u)\qquad
\text{ in } \mathbb{R}^N \] where $N\geq 1$, $I_\alpha$ is the Riesz potential
of order $\alpha \in (0, N)$, the exponent $\frac{\alpha}{N}+1$ is critical
with respect to the Hardy--Littlewood--Sobolev inequality and the nonlinear
perturbation $f$ satisfies suitable growth and structural assumptions. 查看全文>>