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arXiv · 2604.05486

Positive Solutions for a Mixed Local-Nonlocal Problem with Semipositone Nonlinearity

Komal Verma·Gaurav Dwivedi
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Abstract

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} -\Delta_p u+ (-\Delta)^s_p u &= \lambda f(u) && \text{in } \Omega, u &= 0 && \text{in } \mathbb{R}^N \setminus \Omega, \end{aligned} \right. \end{equation*} using mountain pass arguments, comparison principles and regularity principles.

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Komal Verma, Gaurav Dwivedi. 2026-04-07. Positive Solutions for a Mixed Local-Nonlocal Problem with Semipositone Nonlinearity. https://arxiv.org/abs/2604.05486

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