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Journal of Function Spaces
Volume 2017, Article ID 3793872, 7 pages
https://doi.org/10.1155/2017/3793872
Research Article

Existence and Multiplicity of Nontrivial Solutions for a Class of Semilinear Fractional Schrödinger Equations

School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China

Correspondence should be addressed to Xinsheng Du; moc.361@7791gnehsnixud

Received 11 May 2017; Accepted 21 August 2017; Published 26 September 2017

Academic Editor: Yong H. Wu

Copyright © 2017 Xinsheng Du and Anmin Mao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the existence of solutions to the following fractional Schrödinger type equations: , where the primitive of the nonlinearity is of superquadratic growth near infinity in and the potential is allowed to be sign-changing. By using variant Fountain theorems, a sufficient condition is obtained for the existence of infinitely many nontrivial high energy solutions.