Normalized Solutions for Schrodinger-Poisson Type Systems with Critical Nonlocal Term

This paper focuses on the existence of normalized ground state solution for Schrodinger-Poisson system with doubly critical growth {-Delta u - phi|u|(3)u = lambda u + f(u) + |u|(4)u, x is an element of R-3, -Delta phi = |u|(5), x is an element of R-3, having prescribed mass integral(3)(R)|u|(2)dx = m(2), where m > 0 is a constant, lambda is an element of R is unknown and appears as a Lagrange multiplier, f is a nonlinear term of Sobolev subcritical and is mass supercritical. We show that there exists a normalized ground state solution for the above system when the mass m is large enough. In addition, we also discuss the continuity and monotonicity of the ground state energy E-m, and explain the asymptotic property of E-m when m is large enough. Our studies complement and extend the researches of Meng and He (Methods Nonlinear Anal 62:509-534, 2023), in the sense we deal with the effect of mass-changing on the existence of normalized solutions.