Existence of positive solutions for a quasilinear Schrödinger equation. (December 2018)

• Record Type: Journal Article
• Authors: Chu, Changmu; Liu, Haidong
• Is Part Of: Nonlinear analysis. Volume 44(2018)
• Page Start: 118
• Page End: 127
• Publication Date: 2018-12
• Subjects: Quasilinear Schrödinger equation -- Radial potential -- Change of variables -- Monotonicity trick -- A priori estimate; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.04.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with the quasilinear Schrödinger equation (0.1) − Δ u + V ( x ) u − Δ [ ( 1 + u 2 ) 1 2 ] u 2 ( 1 + u 2 ) 1 2 = μ h ( u ) in R N, where N ≥ 3 and μ > 0 is a parameter. Under some appropriate assumptions on the potential V and the nonlinear term h, we establish the existence of a positive solution for (0.1) with sufficiently large μ . Our method is based on a change of variables, monotonicity trick developed by Jeanjean and a priori estimate.