Author(s)

Chunliu Liu

School of Mathematical Sciences, Tiangong University, Tianjin, China.

In this paper, we look for solutions to the following Schrödinger-Bopp-Podolsky system with prescribed L²-norm constraint , where q ≠ 0, a, ρ > 0 are 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 .

Schrödinger-Bopp-Podolsky System, Standing Waves, Normalized Solution, Orbital Stability

Liu, C. (2022) Existence and Stability of Standing Waves with Prescribed L²-Norm for a Class of Schrödinger-Bopp-Podolsky System. Journal of Applied Mathematics and Physics, 10, 2245-2267. doi: 10.4236/jamp.2022.107154.