A Unified Topological Analysis of Variable Growth Kirchhoff-Type Equations
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908834360983552 |
|---|---|
| author | Goodrich, Christopher S. Nakhl, Gabriel |
| author_facet | Goodrich, Christopher S. Nakhl, Gabriel |
| contents | We consider a nonlocal differential equation of Kirchhoff type with a convolution coefficient involving variable growth. The novelty of our work lies in allowing a variable exponent in the nonlocal term. By relating the variable growth problem to a corresponding constant growth problem, we establish the existence of at least one positive solution subject to boundary conditions. Our approach relies on topological fixed point theory. The results treat convex, concave, and mixed growth regimes, providing a unified framework for one-dimensional Kirchhoff-type problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13225 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Topological Analysis of Variable Growth Kirchhoff-Type Equations Goodrich, Christopher S. Nakhl, Gabriel Analysis of PDEs Functional Analysis Primary 34B10, 34B18 Secondary 33B15, 42A85, 44A35, 26A33, 46E35, 47H30 We consider a nonlocal differential equation of Kirchhoff type with a convolution coefficient involving variable growth. The novelty of our work lies in allowing a variable exponent in the nonlocal term. By relating the variable growth problem to a corresponding constant growth problem, we establish the existence of at least one positive solution subject to boundary conditions. Our approach relies on topological fixed point theory. The results treat convex, concave, and mixed growth regimes, providing a unified framework for one-dimensional Kirchhoff-type problems. |
| title | A Unified Topological Analysis of Variable Growth Kirchhoff-Type Equations |
| topic | Analysis of PDEs Functional Analysis Primary 34B10, 34B18 Secondary 33B15, 42A85, 44A35, 26A33, 46E35, 47H30 |
| url | https://arxiv.org/abs/2602.13225 |