On singular quasilinear Schrödinger equations with critical exponents. (1st March 2017)

• Record Type: Journal Article
• Authors: Wang, Youjun; Li, Zhouxin; Abdelgadir, Ahmed Adam
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 14(2017)
• Page Start: 5095
• Page End: 5108
• Publication Date: 2017-03-01
• Subjects: quasilinear Schrödinger equations -- concentration–compactness -- critical exponents; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4373
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We consider a class of singular quasilinear Schrödinger equations of the form − Δ u − λ V ( x ) u − α 2 Δ ( | u | α ) | u | α − 2 u = K ( x ) | u | 2 ∗ − 2 u, x ∈ R N, where V ( x ), K ( x ) : R N → R are given functions, N ⩾3, λ is a positive constant, 0 < α < 1, 2 ∗ = 2 N N − 2 . By using variational methods together with concentration–compactness principle, we prove the existence of positive solutions of the aforementioned equations under suitable conditions on V ( x ) and K ( x ). Copyright © 2017 John Wiley & Sons, Ltd.