Existence of solutions for a class of Kirchhoff-type equations with indefinite potential

2024/03/28 by Linlian Xiao, Jiaqian Yuan, Xiao, Linlian +5
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2403.19284

openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the existence of solutions of the following Kirchhoff-type problem \ -(a+b∫_ℝ³|∇ u|²dx)Δu+ V(x)u=f(x,u),~\rmin~ ℝ³,
u∈ H¹(ℝ³), . where a,b are postive constants, and the potential V(x) is continuous and indefinite in sign. Under some suitable assumptions on V(x) and f, we obtain the existence of solutions by the Symmetric Mountain Pass Theorem.

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