Existence of positive solutions for a class of quasilinear Schrodinger equations with local superlinear nonlinearities

This paper discusses the following class of quasilinear Schrodinger equations -Delta u + V(x)u + kappa/2 [Delta(u(2))]u = lambda l(u), x is an element of R-N, where N >= 3, lambda > 0, and kappa is an element of R \ {0}. With some appropriate assumptions on the potential V and local assumptions on the nonlinear term l, we determine that positive solutions to the above equation exist by using the ingenious monotonicity trick developed by Jeanjean and minimax techniques with careful L-infinity-estimates. (C) 2019 Elsevier Inc. All rights reserved.