Taiwanese Journal of Mathematics

INFINITELY MANY SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER EQUATIONS

Jing Chen and X. H. Tang

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Abstract

In this paper, we deal with the existence of infinitely many solutions for a class of sublinear Schrödinger equation $$ \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \ \ \ \ x\in {\mathbb{R}}^{N},\\ u\in H^{1}({\mathbb{R}}^{N}). \end{array} \right. $$ Under the assumptions that $\inf_{{\mathbb{R}}^{N}}V(x) \gt 0$ and $f(x, t)$ is indefinite sign and sublinear as $|t|\to +\infty$, we establish some existence criteria to guarantee that the above problem has at least one or infinitely many nontrival solutions by using the genus properties in critical point theory.

Article information

Source
Taiwanese J. Math. Volume 19, Number 2 (2015), 381-396.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133636

Digital Object Identifier
doi:10.11650/tjm.19.2015.4044

Zentralblatt MATH identifier
1357.35159

Subjects
Primary: 35J10: Schrödinger operator [See also 35Pxx] 35J20: Variational methods for second-order elliptic equations

Keywords
Schrödinger equation sublinear genus indefinite sign

Citation

Chen, Jing; Tang, X. H. INFINITELY MANY SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER EQUATIONS. Taiwanese J. Math. 19 (2015), no. 2, 381--396. doi:10.11650/tjm.19.2015.4044. https://projecteuclid.org/euclid.twjm/1499133636


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