A note on nonlocal discrete problems involving sign-changing Kirchhoff functions

2025/05/19 by Biagio Ricceri, Ricceri, Biagio
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2505.12790

openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we establish a multiplicity theorem for a nonlocal discrete problem of the type \cases-(a∑_m=1ⁿ⁺¹|x_m-x_m-1|²+b)(x_k+1-2x_k+x_k-1)=h_k(x_k)\hskip 10pt k=1,...,n, \cr amp; \cr x₀=x_n+1=0\cr assuming a>0 and (for the first time) b<0.

Citations

• Multiple critical points in closed sets via minimax theorems
• Existence, uniqueness, localization and minimization property of positive solutions for non-local problems involving discontinuous Kirchhoff functions
• Multiplicity theorems involving functions with non-convex range

Related

• Positive solutions for Kirchhoff problems with vanishing nonlocal term
• A multiplicity result for nonlocal problems involving nonlinearities with bounded primitive
• Multiplicity result for mixed local and nonlocal Kirchhoff problem involving critical growth
• On an open question of Ricceri concerning a Kirchhoff-type problem
• A note on multiple solutions for Kirchhoff-type equations with a Neumann condition