Infinitely many solutions for a class of elliptic boundary value problems with (p,q)-Kirchhoff type

2025/04/28 by Zongxi Li, Li, Zongxi, Weiya Qi +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2504.19576

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the existence of infinitely many solutions for the following elliptic boundary value problem with (p,q)-Kirchhoff type \begincases -[M₁(∫_Ω|∇ u₁|^p dx)]^p-1Δ_p u₁+[M₃(∫_Ωa₁(x)|u₁|^p dx)]^p-1a₁(x)|u₁|^p-2u₁=G_u1(x,u₁,u₂) in Ω, -[M₂(∫_Ω|∇ u₂|^q dx)]^q-1Δ_q u₂+[M₄(∫_Ωa₂(x)|u₂|^q dx)]^q-1a₂(x)|u₂|^q-2u₂=G_u2(x,u₁,u₂) in Ω, u₁=u₂=0 on ∂Ω. \endcases By using a critical point theorem due to Ding in [Y. H. Ding, Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems. Nonlinear Anal, 25(11)(1995)1095-1113], we obtain that system has infinitely many solutions under the sub-(p,q) conditions.

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