A Fixed Point Theorem for Systems of Nonlinear Operator Equations and Applications to $$(p_1, p_2)$$ ( p 1 , p 2 ) -Laplacian System

Abstract

A new fixed point theorem for systems of nonlinear operator equations is established by means of topological degree theory and positively 1-homogeneous operator, where the components has a positively 1-homogeneous majorant or minorant. As applications, the existence of positive solutions for $$(p_1, p_2)$$ -Laplacian system is considered under some conditions concerning the positive eigenvalues corresponding to the relevant positively 1-homogeneous operators.