Positive solution for the (p, q)-Laplacian systems by a new version of sub-super solution method

Abstract

PurposeIn this paper, the authors give a new version of the sub-super solution method and prove the existence of positive solution for a (p, q)-Laplacian system under weak assumptions than usually made in such systems. In particular, nonlinearities need not be monotone or positive.Design/methodology/approachThe authors prove that the sub-super solution method can be proved by the Shcauder fixed-point theorem and use the method to prove the existence of a positive solution in elliptic systems, which appear in some problems of population dynamics.FindingsThe results complement and generalize some results already published for similar problems.Originality/valueThe result is completely new and does not appear elsewhere and will be a reference for this line of research.