Normalized solutions for Schrödinger–Bopp–Podolsky systems with general nonlinearities of mass subcritical

In this paper, we investigate the existence and nonexistence of normalized solutions for the following nonlinear Schrödinger–Bopp–Podolsky system −Δu + ϕu = λu + f(u) and −Δϕ + a2Δ2ϕ = 4πu2 in R3 with an L2 constraint ∫R3u2dx=c>0, where a > 0, λ∈R will arise as a Lagrange multiplier and f∈C(R,R) satisfies general mass subcritical growth conditions which cover the case f(u) = |u|p−2u with p∈(2,103). Moreover, the asymptotic behavior of normalized solutions is established as a → 0 when f is super-quadratic growth at infinity. Finally, replacing ϕu by −ϕu in the above system, we also study the existence of normalized solutions when f satisfies some suitable mass subcritical conditions.