Taiwanese Journal of Mathematics

MULTIPLE SOLUTIONS FOR PERIODIC SCHRÖDINGER EQUATIONS WITH SPECTRUM POINT ZERO

Dongdong Qin, Fangfang Liao, and Yi Chen

Full-text: Open access

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.

Article information

Source
Taiwanese J. Math., Volume 18, Number 4 (2014), 1185-1202.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706484

Digital Object Identifier
doi:10.11650/tjm.18.2014.3451

Mathematical Reviews number (MathSciNet)
MR3245437

Zentralblatt MATH identifier
1357.35161

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Keywords
Schrödinger equation spectrum point zero infinitely many solutions

Citation

Qin, Dongdong; Liao, Fangfang; Chen, Yi. MULTIPLE SOLUTIONS FOR PERIODIC SCHRÖDINGER EQUATIONS WITH SPECTRUM POINT ZERO. Taiwanese J. Math. 18 (2014), no. 4, 1185--1202. doi:10.11650/tjm.18.2014.3451. https://projecteuclid.org/euclid.twjm/1499706484


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