## Taiwanese Journal of Mathematics

### NEW CONDITIONS ON SOLUTIONS FOR PERIODIC SCHRÖDINGER EQUATIONS WITH SPECTRUM ZERO

#### Abstract

This paper is concerned with the following Schrödinger equation:$\begin{cases}-\triangle u + V(x)u = f(x, u), &\textrm{for x \in \mathbb{R}^{N}}, \\u(x) \to 0, &\textrm{as |x| \to \infty},\end{cases}$ 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 new technique for showing the boundedness of Cerami sequences, we are able to obtain the existence of nontrivial solutions with mild assumptions on $f$.

#### Article information

Source
Taiwanese J. Math., Volume 19, Number 4 (2015), 977-993.

Dates
First available in Project Euclid: 4 July 2017

https://projecteuclid.org/euclid.twjm/1499133685

Digital Object Identifier
doi:10.11650/tjm.19.2015.4227

Mathematical Reviews number (MathSciNet)
MR3384675

Zentralblatt MATH identifier
1357.35162

#### Citation

Qin, Dongdong; Tang, Xianhua. NEW CONDITIONS ON SOLUTIONS FOR PERIODIC SCHRÖDINGER EQUATIONS WITH SPECTRUM ZERO. Taiwanese J. Math. 19 (2015), no. 4, 977--993. doi:10.11650/tjm.19.2015.4227. https://projecteuclid.org/euclid.twjm/1499133685

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