On the antimaximum principle for the \(p\)-Laplacian with indefinite weight
This paper is devoted to the study of the antimaximum principle (AMP) for the problem \[ \begin{gathered} -\Delta_p u=\lambda m(x)|u|^{p-2} u+ h(x)\quad\text{in }\Omega,\\ Bu= 0\quad\text{on }\partial\Omega,\end{gathered} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\), \(\Delta_p\) is the \(p\)-Laplacian and \(Bu= 0\) represents either the Dirichlet or the Neumann homogeneous boundary conditions. The authors show that under suitable assumption on \(m(x)\), \(h(x)\) AMP holds.
scientific article; zbMATH DE number 1810001
scientific article