New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory
- 1 January 2021
- journal article
- research article
- Published by University of Szeged in Electronic Journal of Qualitative Theory of Differential Equations
- No. 73,p. 1-17
- https://doi.org/10.14232/ejqtde.2021.1.73
Abstract
In this paper, we study the following quasilinear Schrödinger equation − Δ u + V ( x ) u − κ u Δ ( u 2 ) + μ h 2 ( | x | ) | x | 2 ( 1 + κ u 2 ) u + μ ( ∫ | x | + ∞ h ( s ) s ( 2 + κ u 2 ( s ) ) u 2 ( s ) d s ) u = f ( u ) in R 2 , κ > 0 V ∈ C 1 ( R 2 , R ) and f ∈ C ( R , R ) By using a constraint minimization of Pohožaev–Nehari type and analytic techniques, we obtain the existence of ground state solutions.Keywords
This publication has 33 references indexed in Scilit:
- Energy Solution to the Chern-Simons-Schrödinger EquationsAbstract and Applied Analysis, 2013
- Standing waves of nonlinear Schrödinger equations with the gauge fieldJournal of Functional Analysis, 2012
- Standing waves of the Schrödinger equation coupled with the Chern-Simons gauge fieldJournal of Mathematical Physics, 2012
- Existence of solutions for a quasilinear Schrödinger equation with subcritical nonlinearitiesNonlinear Analysis, 2012
- Existence of ground states for a modified nonlinear Schrödinger equationNonlinearity, 2010
- Solutions for Quasilinear Schrödinger Equations via the Nehari MethodCommunications in Partial Differential Equations, 2004
- Soliton solutions to the gauged nonlinear Schrödinger equation on the planePhysical Review Letters, 1990
- Regularity for a more general class of quasilinear elliptic equationsJournal of Differential Equations, 1984
- Existence of solitary waves in higher dimensionsCommunications in Mathematical Physics, 1977
- On harnack type inequalities and their application to quasilinear elliptic equationsCommunications on Pure and Applied Mathematics, 1967