TITLE:
Existence and Stability of Standing Waves with Prescribed L2-Norm for a Class of Schrödinger-Bopp-Podolsky System
AUTHORS:
Chunliu Liu
KEYWORDS:
Schrödinger-Bopp-Podolsky System, Standing Waves, Normalized Solution, Orbital Stability
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.7,
July
28,
2022
ABSTRACT: In this paper, we look for solutions to the following Schrödinger-Bopp-Podolsky system with prescribed L2-norm constraint , where q ≠ 0, a, ρ > 0are constants. At first, by the classical minimizing argument, we obtain a ground state solution to the above problem for sufficiently small ρ when . Secondly, in the case p = 6, we show the nonexistence of positive solutions by using a Liouville-type result. Finally, we argue by contradiction to investigate the orbital stability of standing waves for .