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.
Citation
Jing Chen. X. H. Tang. "INFINITELY MANY SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER EQUATIONS." Taiwanese J. Math. 19 (2) 381 - 396, 2015. https://doi.org/10.11650/tjm.19.2015.4044
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