Existence and Multiplicity of Normalized Solutions to Schrödinger Equations with General Nonlinearities in Bounded Domains

This paper focuses on the existence of multiple normalized solutions to Schrödinger equations with general nonlinearities in bounded domains via variational methods. We first obtain two positive normalized solutions, one is a normalized ground state by searching for a local minimizer, and the other one is a mountain pass solution. Secondly, using a version of Linking theorems for normalized solutions, we prove the multiplicity of solutions to Schrödinger equations in a star-shaped bounded domain. Moreover, we arrive at the existence of nonradial normalized solutions to Schrödinger equations in a ball.