Normalized Solutions for Schrödinger-Bopp-Podolsky Systems in Bounded Domains with General Nonlinearities
Authors
Kai Sheng
Abstract
In this paper, by adapting the perturbation method, we study normalized standing wave solutions for the following nonlinear Schrödinger-Bopp-Podolsky system:
- Delta u + q(x) phi u = omega u + f(u) in Omega, - Delta phi + a^2 Delta^2 phi = q(x) u^2 in Omega,
where Omega is a smooth bounded domain in R^3, a > 0, and omega is the Lagrange multiplier associated with the L^2 mass constraint integral over Omega of u^2 equals mu, and f: R -> R is a continuous function satisfying some technical conditions. In particular, we prove the existence of normalized solutions for all masses mu in an interval (0, mu_0), under either Navier or Neumann boundary conditions for phi. Moreover, when f is odd, we obtain multiplicity of normalized solutions; and if Omega is star-shaped, we further obtain a normalized ground state solution.
