Normalized Solutions to Kirchhoff Equation with Nonnegative Potential

Abstract

This paper is concerned with the existence of solutions to the problemwhere a, b > 0 are constants, V ≥ 0 is a potential, N ≥ 1, and p ∈ (2 + 4 N , 2 * ). We use a more subtle analysis to revisit the limited problem(V ≡ 0), and obtain a new energy inequality and bifurcation results. Based on these observations, we establish the existence of bound state normalized solutions under different assumptions on V . These conclusions extend some known results in previous papers.