@article{Wang_Zhang_Chen_2015, title={Standing waves for nonlinear Schrödinger-Poisson equation with high frequency}, volume={45}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2015.028}, DOI={10.12775/TMNA.2015.028}, abstractNote={We study the existence of ground state and<br />bound state for the following Schrödinger-Poisson equation<br />where $p\in(3,5)$, $\lambda > 0$, $V\in<br />C(\mathbb{R}^3,\mathbb{R}^+)$ and $\lim\limits_{|x|\to<br />+\infty}V(x)=\infty$. By using  variational method, we prove that<br />for any $\lambda > 0$, there exists $\delta_1(\lambda) > 0$ such that<br />for $\mu_1 < \mu < \mu_1 + \delta_1(\lambda)$, problem (P) has  a nonnegative<br />ground state with negative energy, which bifurcates from zero solution; problem (P) has a nonnegative bound state with<br />positive energy, which can not bifurcate from zero solution. Here $\mu_1$ is the first eigenvalue of $-\Delta<br />+V$. Infinitely many nontrivial bound states are also obtained with<br />the help of a generalized version of symmetric mountain pass<br />theorem.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Wang, Zhengping and Zhang, Xiaoju and Chen, Jianqing}, year={2015}, month={Jun.}, pages={601–614} }