Normalized solutions for Quasilinear Schrödinger-Possion systems in bounded domains with general nonlinearities

In this paper, by adapting the perturbation method, we study normalized standing wave solutions for the following nonlinear Schrödinger-Bopp-Podolsky system: { – ∆ u + ϕ u = G u + f ( u ) in Ω , – ∆ ϕ – ε 4 ∆ 4 ϕ = u 2 in Ω , u = ϕ = 0 on ∂ Ω , where Ω ⊂ R 3 is a smooth bounded domain, a >0, G∈R is the Lagrange multiplier associated with the L 2 -mass constraint ∫ Ω u 2 d x = µ , and f :R→R is a continuous function satisfying some technical conditions. In particular, we prove the existence of normalized solutions for small µ . Moreover, when f is odd, we obtain multiplicity of normalized solutions.