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Semiclassical states for fractional Schrödinger equations with critical nonlinearities
  • +1
  • Ying lv,
  • Dai Ting-ting,
  • Jia-Lu Du,
  • Zeng-Qi Ou
Ying lv
Southwest University School of Mathematics and Statistics

Corresponding Author:ly0904@swu.edu.cn

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Dai Ting-ting
Southwest University School of Mathematics and Statistics
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Jia-Lu Du
Southwest University School of Mathematics and Statistics
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Zeng-Qi Ou
Southwest University School of Mathematics and Statistics
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Abstract

In this paper, we consider the following fractional Schrödinger equation ε 2 s ( − ∆ ) s u + V ( x ) u = P ( x ) f ( u ) + Q ( x ) | u | 2 s ∗ − 2 u in R N , where ε>0 is a parameter, s∈(0 ,1), 2 s ∗ = 2 N N − 2 s , N>2 s, ( − ∆ ) s is the fractional Lapalacian and f is a superlinear and subcritical nonlinearity. Under a local condition imposed on the potential function, combining the penalization method and the concentration-compactness principle, we prove the existence of a positive solution for the above equations.
05 Jun 2023Submitted to Mathematical Methods in the Applied Sciences
06 Jun 2023Submission Checks Completed
06 Jun 2023Assigned to Editor
21 Jun 2023Review(s) Completed, Editorial Evaluation Pending
23 Jun 2023Reviewer(s) Assigned
06 Sep 2023Editorial Decision: Revise Minor
27 Sep 20231st Revision Received
28 Sep 2023Submission Checks Completed
28 Sep 2023Assigned to Editor
28 Sep 2023Review(s) Completed, Editorial Evaluation Pending
30 Sep 2023Reviewer(s) Assigned
06 Oct 2023Editorial Decision: Accept