Ground state solutions for fractional Schrödinger equations with critical Sobolev exponent

Kaimin Teng; Xiumei  He

doi:10.3934/cpaa.2016.15.991

Article Contents

2016, Volume 15, Issue 3: 991-1008. Doi: 10.3934/cpaa.2016.15.991

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Ground state solutions for fractional Schrödinger equations with critical Sobolev exponent

Kaimin Teng^1, and
Xiumei He^2,

1.
Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024
2.
Department of Mathematics, Kunming University, Kunming, Yunnan 650214

Received: October 2015

Revised: December 2015

Published: May 2016

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Abstract

In this paper, we establish the existence of ground state solutions for fractional Schrödinger equations with a critical exponent. The methods used here are based on the $s-$harmonic extension technique of Caffarelli and Silvestre, the concentration-compactness principle of Lions and methods of Brezis and Nirenberg.

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Mathematics Subject Classification: Primary: 34C25, 58E30; Secondary: 47H04.

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