Liu, S. and Zhou, J. (2018) Standing Waves for Quasilinear Schrödinger Equations with Indefinite Potentials. Journal of Differential Equations, 265, 3970-3987.
https://doi.org/10.1016/j.jde.2018.05.024

has been cited by the following article:

• 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.