Positive solutions for equations and systems with $p$-Laplace like operators

Abstract

We prove the existence of positive solutions to boundary-value problems of the form \begin{align*} \begin{gathered} (\phi(u'))'+f(t,u)=0,\quad t\in(0,1)\\ \theta(u(0))=\beta \theta(u'(0)), \quad \theta(u(1))=-\delta \theta(u'(1)), \quad \beta,\delta\ge 0, \end{gathered} \end{align*} where $\phi$ and $\theta$ are odd increasing homeomorphisms of the real line. We also prove the existence of positive solutions to related systems. Our approach is via a priori estimates and Leray-Schauder degree.