Electron. J. Differential Equations, Vol. 2018 (2018), No. 97, pp. 1-13.

Infinitely many solutions for sublinear fractional Schrodinger-type equations with general potentials

Gang-Ling Hou, Bin Ge, Jian-Fang Lu

Abstract:
This article concerns the fractional Schrodinger type equations
$$ (-\Delta)^\alpha u+V(x)u =f(x,u) \quad\text{in } \mathbb{R}^N, $$
where $N\geq 2$, $\alpha\in(0,1)$, $(-\Delta)^\alpha$ stands for the fractional Laplacian, $V$ is a positive continuous potential, $f\in C(\mathbb{R}^N\times\mathbb{R},\mathbb{R})$. We establish criteria that guarantee the existence of infinitely many solutions by using the genus properties in critical point theory.

Submitted January 27, 2018. Published April 24, 2018.
Math Subject Classifications: 26A33, 35J60, 47J30.
Key Words: Fractional Laplacian; variational method; sublinear; genus.

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Gang-Ling Hou
College of Aerospace and Civil Engineering
Harbin Engineering University
Harbin, 150001, China
email: hougl@hrbeu.edu.cn
Bin Ge
Department of Applied Mathematics
Harbin Engineering University
Harbin, 150001, China
email: gebin791025@hrbeu.edu.cn
Jian-Fang Lu
Department of Applied Mathematics
Harbin Engineering University
Harbin, 150001, China
email: 1176678630@qq.com

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