Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774049 | Journal of Differential Equations | 2017 | 33 Pages |
Abstract
In this article, we first employ the concentration compactness techniques to prove existence and stability results of standing waves for nonlinear fractional Schrödinger-Choquard equationiâtΨ+(âÎ)αΨ=a|Ψ|sâ2Ψ+λ(1|x|Nâβâ|Ψ|p)|Ψ|pâ2ΨinRN+1, where Nâ¥2, αâ(0,1), βâ(0,N), sâ(2,2+4αN), pâ[2,1+2α+βN), and the constants a, λ are nonnegative satisfying a+λâ 0. We then extend the arguments to establish similar results for coupled standing waves of nonlinear fractional Schrödinger systems of Choquard type. The same argument works for equations with an arbitrary number of combined nonlinearities and when |x|βâN is replaced by a more general convolution potential K:RNâ[0,â) under certain assumptions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Santosh Bhattarai,