Taiwanese Journal of Mathematics

NEW CONDITIONS ON SOLUTIONS FOR PERIODIC SCHRÖDINGER EQUATIONS WITH SPECTRUM ZERO

Dongdong Qin and Xianhua Tang

Full-text: Open access

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

Permanent link to this document
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

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Keywords
Schrödinger equation strongly indefinite functional spectrum point zero superlinear

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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