Positive solutions for quasilinear Schrödinger equations with superlinear term. Issue 6 (2nd June 2020)

• Record Type: Journal Article
• Authors: Li, Guofa; Huang, Yisheng; Liu, Zeng
• Is Part Of: Complex variables and elliptic equations. Volume 65:Issue 6(2020)
• Page Start: 936
• Page End: 955
• Publication Date: 2020-06-02
• Subjects: B. Zhang; Quasilinear Schrödinger equations -- mountain pass theorem -- positive solutions; 35J20 -- 35J62; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2019.1636791
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: In this paper, we study the following quasilinear Schrödinger equation − d i v ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = h ( u ), x ∈ R N, where N ≥ 3, V ∈ C ( R N, R + ) is a given potential, g is a C 1 even function with g ′ ( t ) ≤ 0 for all t ≥ 0, g ( 0 ) = 1, lim t → + ∞ g ( t ) = a, 0 < a < 1 . The nonlinearity h ∈ C ( R, R ) satisfies superlinear growth at infinity. We get existence results of the positive solution for the above problem. Moreover, we give two applications of our results, which improves recent results in Alves et al. [Soliton solutions for a class of quasilinear Schrödinger equations with a parameter. J Differ Equ. 2015;259:318–343].