Abstract
This paper is concerned with the following Schrödinger equation: $$ \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \ \ \ x\in\mathbb R^N,\\ u(x)\rightarrow0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ as \ \ \ \ |x| \rightarrow\infty, \end{array} \right. $$ where the potential $V$ and $f$ are periodic with respect to $x$ and $0$ is a boundary point of the spectrum $\sigma(-\triangle+V)$. By a generalized variant fountain theorem and an approximation technique, for old $f$, we are able to obtain the existence of infinitely many large energy solutions.
Citation
Dongdong Qin. Fangfang Liao. Yi Chen. "MULTIPLE SOLUTIONS FOR PERIODIC SCHRÖDINGER EQUATIONS WITH SPECTRUM POINT ZERO." Taiwanese J. Math. 18 (4) 1185 - 1202, 2014. https://doi.org/10.11650/tjm.18.2014.3451
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