Standing waves for nonlinear Schrödinger-Poisson equation with high frequency
DOI:
https://doi.org/10.12775/TMNA.2015.028Keywords
Schrödinger-Poisson equation, ground states, bound states, variational methodAbstract
We study the existence of ground state andbound state for the following Schrödinger-Poisson equation
where $p\in(3,5)$, $\lambda > 0$, $V\in
C(\mathbb{R}^3,\mathbb{R}^+)$ and $\lim\limits_{|x|\to
+\infty}V(x)=\infty$. By using variational method, we prove that
for any $\lambda > 0$, there exists $\delta_1(\lambda) > 0$ such that
for $\mu_1 < \mu < \mu_1 + \delta_1(\lambda)$, problem (P) has a nonnegative
ground state with negative energy, which bifurcates from zero solution; problem (P) has a nonnegative bound state with
positive energy, which can not bifurcate from zero solution. Here $\mu_1$ is the first eigenvalue of $-\Delta
+V$. Infinitely many nontrivial bound states are also obtained with
the help of a generalized version of symmetric mountain pass
theorem.
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Published
2015-06-01
How to Cite
1.
WANG, Zhengping, ZHANG, Xiaoju and CHEN, Jianqing. Standing waves for nonlinear Schrödinger-Poisson equation with high frequency. Topological Methods in Nonlinear Analysis. Online. 1 June 2015. Vol. 45, no. 2, pp. 601 - 614. [Accessed 12 December 2024]. DOI 10.12775/TMNA.2015.028.
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