Positive Solutions for a Mixed Local-Nonlocal Problem with Semipositone Nonlinearity
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910107592294400 |
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| author | Verma, Komal Dwivedi, Gaurav |
| author_facet | Verma, Komal Dwivedi, Gaurav |
| contents | In this article, we prove the existence of at least one positive solution for the mixed local-nonlocal semipositone problem \begin{equation*}
\left\{
\begin{aligned}
-Δ_p u+ (-Δ)^s_p u &= λf(u) && \text{in } Ω,
u &= 0 && \text{in } \mathbb{R}^N \setminus Ω,
\end{aligned}
\right. \end{equation*}
using mountain pass arguments, comparison principles and regularity principles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05486 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Positive Solutions for a Mixed Local-Nonlocal Problem with Semipositone Nonlinearity Verma, Komal Dwivedi, Gaurav Analysis of PDEs 35J20, 35J60, 35J92, 35B09 In this article, we prove the existence of at least one positive solution for the mixed local-nonlocal semipositone problem \begin{equation*} \left\{ \begin{aligned} -Δ_p u+ (-Δ)^s_p u &= λf(u) && \text{in } Ω, u &= 0 && \text{in } \mathbb{R}^N \setminus Ω, \end{aligned} \right. \end{equation*} using mountain pass arguments, comparison principles and regularity principles. |
| title | Positive Solutions for a Mixed Local-Nonlocal Problem with Semipositone Nonlinearity |
| topic | Analysis of PDEs 35J20, 35J60, 35J92, 35B09 |
| url | https://arxiv.org/abs/2604.05486 |