Existence of positive solutions for a quasilinear Schrödinger equation. (December 2018) - Chu, Changmu; Liu, Haidong
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.