Positive Solutions for Nonlinear Nonhomogeneous Robin Problems

Abstract

We consider a nonlinear, nonhomogeneous Robin problem with a Carathéodory reaction which satisfies certain general growth conditions near $0^{+}$ and near $+\infty$. We show the existence and regularity of positive solutions, the existence of a smallest positive solution and under an additional condition on the reaction, we show the uniqueness of the positive solutions. We then show that our setting incorporates certain parametric Robin equations of interest such as nonlinear equidiffusive logistic equations.