Normalized Solutions to Kirchhoff Equation with Nonnegative Potential

2023/01/19 by Shuai Mo, Shiwang Ma, Mo, Shuai +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.07926

openalex publication_date 2023/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the existence of solutions to the problem -(a+ b∫_ℝ^N|∇ u|² dx )Δu +V(x)u+λu = |u|^p-2u, x ∈ ℝ^N, λ∈ ℝ⁺ where 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.

Related

• Normalized Solutions to Nonautonomous Kirchhoff Equation
• Kirchhoff-Schrödinger equations in ℝ² with critical exponential growth and indefinite potential
• Normalized solution for Kirchhoff equation with upper critical exponent and mixed Choquard type nonlinearities
• Normalized solutions to Kirchhoff type equations with a critical growth nonlinearity
• Normalized solutions to a class of Kirchhoff equations with Sobolev critical exponent