Existence and a priori estimates for positive solutions of \(p\)-Laplace systems (Q701093)

The authors deal with \(p\)-Laplace systems of the form \[ \begin{gathered} -\Delta_{p_1}u= f(|v|)\quad\text{in }\Omega,\\ -\Delta_{p_2} u= g(|u|)\;\text{in}\;\Omega,\\ u= v= 0\quad\text{on }\partial\Omega,\end{gathered}\tag{1} \] where \(1< p_1\), \(p_2< N\), \(\Omega\subset\mathbb R^N\) is bounded and convex, and \(f,g: \mathbb R\to \mathbb R_+\) are given functions. Under some suitable assumptions on \(f\), \(g\) the authors prove existence and some a priori estimate for solutions of (1). To this end they use continuation and moving hyperplane methods.