A remark on the linearized stability of positive solutions for systems involving the \(p\)-Laplacian
This paper is devoted to the stability properties of positive stationary solutions for nonlinear elliptic systems of the form \[ \begin{gathered} -\Delta_p u=\lambda f(u,v)\quad\text{in }\Omega,\\ -\Delta_pv=\lambda g(u,v)\quad\text{in }\Omega,\\ Bu= 0= Bv\quad\text{on }\partial\Omega,\end{gathered} \] where \(\Delta_p\) denotes the \(p\)-Laplacian, \(p> 2\), \(\Omega\) is a bounded domain in \(\mathbb R^d\) \((d> 1)\) with smooth boundary, \[ Bz(x):= \alpha h(x) z+(1- \alpha){\partial z\over\partial n} \] with \(\alpha\in [0,1]\) is a constant, \(h: \partial\Omega\to \mathbb{R}^+\) satisfying some natural assumptions, \(\lambda> 0\), \(f\), \(g\) are \(C^2\) function on \([0,\infty)\times [0,\infty)\).
scientific article; zbMATH DE number 5162440