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Ground States of some Fractional Schrödinger Equations on ℝN

Part of: Equations and inequalities involving nonlinear operators Elliptic equations and systems

Published online by Cambridge University Press:  27 October 2014

Xiaojun Chang
Xiaojun Chang*
Affiliation:
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, People's Republic of China College of Mathematics, Jilin University, Changchun 130012, Jilin, People's Republic of China, (changxj1982@hotmail.com)
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Abstract

In this paper, we study a time-independent fractional Schrödinger equation of the form (−Δ)su + V(x)u = g(u) in ℝN, where N ≥, s ∈ (0,1) and (−Δ)s is the fractional Laplacian. By variational methods, we prove the existence of ground state solutions when V is unbounded and the nonlinearity g is subcritical and satisfies the following geometry condition:

Keywords

ground statesfractional Schrödinger equationvariational methods

MSC classification

Primary: 35J60: Nonlinear elliptic equations
Secondary: 47J30: Variational methods
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 2 , June 2015 , pp. 305 - 321
Copyright
Copyright © Edinburgh Mathematical Society 2012 

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