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Open Access Research

Infinitely many weak solutions for a fractional Schrödinger equation

Wei Dong1*, Jiafa Xu2 and Zhongli Wei23

Author Affiliations

1 Department of Mathematics, Hebei University of Engineering, Handan 056038, Hebei, China

2 School of Mathematics, Shandong University, Jinan 250100, Shandong, China

3 Department of Mathematics, Shandong Jianzhu University, Jinan 250101, Shandong, China

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Boundary Value Problems 2014, 2014:159  doi:10.1186/s13661-014-0159-6

Published: 12 July 2014

Abstract

In this paper we are concerned with the fractional Schrödinger equation , , where , , stands for the fractional Laplacian of order α, V is a positive continuous potential, and f is a continuous subcritical nonlinearity. We obtain the existence of infinitely many weak solutions for the above problem by the fountain theorem in critical point theory.

Keywords:
fractional Laplacian; subcritical nonlinearity; fountain theorem; weak solution