Positive solutions for generalized quasilinear Schrödinger equations with asymptotically linear nonlinearities. Issue 5 (4th April 2021) - Li, Guofa
ABSTRACT: In this paper, we study the following generalized quasilinear Schrödinger equations − 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 1 ( R, R ) satisfies asymptotically linear at infinity. Under certain assumptions on V, g and h, we give the existence results via variational methods. Moreover, we give an application for our results.