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2015 NEW CONDITIONS ON SOLUTIONS FOR PERIODIC SCHRÖDINGER EQUATIONS WITH SPECTRUM ZERO
Dongdong Qin, Xianhua Tang
Taiwanese J. Math. 19(4): 977-993 (2015). DOI: 10.11650/tjm.19.2015.4227

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 $f$.

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Dongdong Qin. Xianhua Tang. "NEW CONDITIONS ON SOLUTIONS FOR PERIODIC SCHRÖDINGER EQUATIONS WITH SPECTRUM ZERO." Taiwanese J. Math. 19 (4) 977 - 993, 2015. https://doi.org/10.11650/tjm.19.2015.4227

Information

Published: 2015
First available in Project Euclid: 4 July 2017

zbMATH: 1357.35162
MathSciNet: MR3384675
Digital Object Identifier: 10.11650/tjm.19.2015.4227

Subjects:
Primary: 35J20, 35J60, 35Q55

Rights: Copyright © 2015 The Mathematical Society of the Republic of China

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Vol.19 • No. 4 • 2015
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