TITLE:
Standing Waves for Quasilinear Schrödinger Equations with Indefinite Nonlinearity
AUTHORS:
Zupei Shen, Haiquan Li
KEYWORDS:
Quasilinear Schrödinger Equations, Indefinite Nonlinearity, Standing Waves
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.5,
May
24,
2021
ABSTRACT: In this article, we consider quasilinear Schrödinger equations of the form Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear Schrödinger equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.