Multiple solutions of Choquard equations in ℝ2 with critical exponential growth via penalization method. (3rd February 2021)

• Record Type: Journal Article
• Authors: Zhang, Hui; Xu, Junxiang
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 8(2021)
• Page Start: 7065
• Page End: 7085
• Publication Date: 2021-02-03
• Subjects: Choquard equation -- critical exponential growth -- multiplicity of solutions -- Nehari manifold -- Trudinger–Moser inequality; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7244
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We deal with the singularly perturbed Choquard equation in the plane with critical exponential growth in the sense of the Trudinger–Moser inequality. Under a local condition imposed on the potential, we show the multiplicity and concentration of positive solutions via penalization technique and variational methods.