Systems of φ-Laplacian three-point boundary-value problems on the positive half-line

Abstract

We study the existence of positive solutions to boundary-value problems for two systems of two second-order nonlinear three-point φ-Laplacian equations defined on the positive half line. The nonlinearities may change sign, exhibit time singularities at the origin, and depend both on the solutions and on their first derivatives. Using the fixed-point theory, we prove some results on the existence of nontrivial positive solutions on appropriate cones in some weighted Banach spaces.