On a class of infinite semipositone problems for (p,q) Laplace operator

Abstract

We analyze a non-linear elliptic boundary value problem, that involves (p, q) Laplace operator, for the existence of its positive solution in an arbitrary smooth bounded domain. The non-linearity here is driven by a continuous function in (0, ∞) which is singular, monotonically increasing and eventually positive. We prove the existence of a positive solution of this problem using a fixed point theorem due to Amann[3]. In addition, for a specific nonlinearity we derive that the obtained solution is maximal in nature. The main results obtained here are first of its kind for a (p, q) Laplace operator in an arbitrary bounded domain.