Entire Sign-Changing Solutions to the Fractional Critical Schrödinger Equation
Year: 2024
Author: Xingdong Tang, Guixiang Xu, Chunyan Zhang, Jihui Zhang
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 3 : pp. 219–248
Abstract
In this paper, we consider the fractional critical Schrödinger equation (FCSE) (−Δ)su−|u|2∗s−2u=0, where u∈˙Hs(RN), N≥4, 0<s<1 and 2∗s=2NN−2s is the critical Sobolev exponent of order s. By virtue of the variational method and the concentration compactness principle with the equivariant group action, we obtain some new type of nonradial, sign-changing solutions of (FCSE) in the energy space ˙Hs(RN). The key component is that we take the equivariant group action to construct several subspace of ˙Hs(RN) with trivial intersection, then combine the concentration compactness argument in the Sobolev space with fractional order to show the compactness property of Palais-Smale sequences in each subspace and obtain the multiple solutions of (FCSE) in ˙Hs(RN).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2024-0006
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 3 : pp. 219–248
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Fractional critical Schrödinger equation sign-changing solution the concentration-compactness principle the equivariant group action the mountain pass theorem.
Author Details
Xingdong Tang Email
Guixiang Xu Email
Chunyan Zhang Email
Jihui Zhang Email