Existence and uniqueness of minimizers for L2‐constrained problems related to fractional Kirchhoff equation. (22nd May 2020)

• Record Type: Journal Article
• Authors: Huang, Xiaomeng; Zhang, Yimin
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 15(2020)
• Page Start: 8763
• Page End: 8775
• Publication Date: 2020-05-22
• Subjects: fractional Kirchhoff equation -- L2‐normalized solutions -- uniqueness; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6543
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we discuss the existence and uniqueness of solutions of the constrained variational problem with respect to the fractional Kirchhoff equation. For the exponent p < p * ( s, N ), a complete classification with respect to p for the existence of solutions of the fractional Kirchhoff functional on the L 2 ‐normalized manifold was given. Furthermore, all these solutions are unique up to translations, and our methods depend only on some simple energy estimates.