Existence of positive solutions for fractional Laplacian systems with critical growth
Date
2022-11-22
Authors
Correia, Jeziel N.
Oliveira, Claudionei
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we show the existence of positive solution to the nonlocal system
(-Δ)s u + α(x)u = 1/2*s Hu(u, v) in ℝN,
(-Δ)s v + b(x)v = 1/2*s Hv(u, v) in ℝN,
u, v > 0 in ℝN,
u, v ∈ Ds,2 (ℝN).
We also prove a global compactness result for the associated energy functional similar to that due to Struwe in [26]. The basic tools are some information from a limit system with a(x) = b(x) = 0, a variant of the Lion's principle of concentration and compactness for fractional systems, and Brouwer degree theory.
Description
Keywords
Fractional Laplacian, Concentration-compactness, Critical nonlinearity global compactness
Citation
Correia, J. N., & Oliveira, C. P. (2022). Existence of positive solutions for fractional Laplacian systems with critical growth. <i>Electronic Journal of Differential Equations, 2022</i>(79), pp. 1-42.
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Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.