1.Department of Statistics and Finance,Shandong University of Science and Technology,Qingdao,People’s Republic of China;2.Shandong Academy of Sciences,Jinan,People’s Republic of China
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.