Regular positive solutions to p-Laplacian systems on unbounded domain

Abstract

This work aims to study the existence and the regularity of positive solutions to a p-Laplacian system with nonlinearities of growth conditions. We focus on positive ground-state solutions and we assume that the nonlinearities are controlled by general polynomial functions, and we use a variational method to apply the mountain pass theorem which guarantees the existence of a super-solution in the sense of Hernandez, then we construct some compact operator T and some invariant set K where we can use the Leray–Schauder fixed point theorem. By the end of this paper, we establish an [Formula: see text]-estimation which allows to derive a property of regularity for such positive solutions.