The Existence of Normalized Solutions for Kirchhoff Equation

Due to the significant applications of the Kirchhoff equation in numerous physical problems, the issue of normalized solutions has gradually attracted the research interest of a large number of scholars in recent years. These studies focus on exploring the existence of normalized solutions to equations, specifically, whether solutions that satisfy the equations can be found under certain mass constraint conditions. An investigation is conducted into the existence of normalized solutions for a class of Kirchhoff equations with combined nonlinear terms. By utilizing the minimization method in variational calculus, along with the concentration compactness principle and the vanishing lemma, it has been proven that under diffusion conditions with arbitrary mass constraints, the equation possesses a normalized solution. Comparing with existing results, the conclusions of the research serve as an extension of existing related results.