| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 14 | |
| Number of page(s) | 19 | |
| DOI | https://doi.org/10.1051/cocv/2023068 | |
| Published online | 01 March 2024 | |
The Effect of Diffusions and Sources on Semilinear Elliptic Problems
1
ICEx – Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627 – Pampulha – CP 702, Belo Horizonte 30161-970, MG, Brazil
2
Universidade Federal da Paraíba, Departamento de Matemática, 58051-900 João Pessoa, Brazil
* Corresponding author: eabreu@ufmg.br
Received:
24
January
2023
Accepted:
19
September
2023
This paper deals with properties of non-negative solutions of the boundary value problem in the presence of diffusion a and source f in a bounded domain Ω ⊂ ℝn, n ≥ 1, where a and f are non-decreasing continuous functions on [0, L0) and f is positive. Part of the results are new even if we restrict ourselves to the Gelfand type case L0 = ∞, a(t) = t and f is a convex function. We study the behavior of related extremal parameters and solutions with respect to L0 and also to a and f in the C0 topology. The work is carried out in a unified framework for 0 < L0 ≤ ∞ under some interactive conditions between a and f
Mathematics Subject Classification: 35J25 / 35B40 / 35J67 / 35J75 / 35K57
Key words: Diffusion problems / existence of solutions / behavior of solutions
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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