## Taiwanese Journal of Mathematics

### INFINITELY MANY SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER EQUATIONS

#### 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

https://projecteuclid.org/euclid.twjm/1499133636

Digital Object Identifier
doi:10.11650/tjm.19.2015.4044

Mathematical Reviews number (MathSciNet)
MR3332303

Zentralblatt MATH identifier
1357.35159

#### 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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