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Ground state solutions of asymptotically linear fractional Schrödinger equations

### Abstract

This paper is devoted to a time-independent fractional Schrödinger equation of the form where N ⩾ 2, s ∈ (0, 1), (−Δ) s stands for the fractional Laplacian. We apply the variational methods to obtain the existence of ground state solutions when f(x, u) is asymptotically linear with respect to u at infinity.

© 2013 AIP Publishing LLC

Received 03 November 2012
Accepted 07 May 2013
Published online 21 June 2013

Acknowledgments:
The author expresses his sincere thanks to Professor Yong Li and Professor Zhi-Qiang Wang for their instructions and many invaluable suggestions. The author is very grateful to Doctor Yixian Gao for helpful discussions. This work is partially supported by NSFC Grant No. 11101178, NSFJP Grant No. 201215184, and FSIIP of Jilin University (Grant No. 201103203).

Article outline:

I. INTRODUCTION AND MAIN RESULTS
II. PRELIMINARIES AND FUNCTIONAL SETTING
III. PROOF OF THEOREM 1.1

/content/aip/journal/jmp/54/6/10.1063/1.4809933

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2013-06-21

2016-05-02

### Abstract

This paper is devoted to a time-independent fractional Schrödinger equation of the form where N ⩾ 2, s ∈ (0, 1), (−Δ) s stands for the fractional Laplacian. We apply the variational methods to obtain the existence of ground state solutions when f(x, u) is asymptotically linear with respect to u at infinity.

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