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

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.