A unified topological analysis of variable growth Kirchhoff-type equations

2025/09/09 by Christopher Goodrich, Christopher S. Goodrich, Gabriel Nakhl · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.1017/prm.2025.10073

openalex publication_date 2025/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Abstract We consider the nonlocal differential equation -A(∫₀¹b(1-s)(u(s))^p(s) ds)u''(t)=λ f(t,u(t)), t∈(0,1), which is a one-dimensional Kirchhoff-like equation with a nonlocal convolution coefficient. The novelty of our work involves allowing a variable growth term in the nonlocal coefficient. By relating the variable growth problem to a constant growth problem, we are able to deduce the existence of at least one positive solution to the differential equation when equipped with boundary data. Our methodology relies on topological fixed point theory. Because our results treat both the convex and concave regimes, together with both the variable growth and constant growth regimes, our results provide a unified framework for one-dimensional Kirchhoff-type problems.

Citations

• Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions
• Nonlocal differential equations with (p,q) (p,q) growth
• Existence and monotonicity of nonlocal boundary value problems: the one-dimensional case
• Existence of solution for a class of nonlocal elliptic problem via sub-supersolution method
• Mathematical modeling of electrorheological materials
• Fractional Differential Equations

Cited by

• Luxemburg Norm Localisation for Nonlocal Differential Equations in Variable Exponent Lebesgue Spaces

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