Ambrosetti–Prodi Alternative for Coupled and Independent Systems of Second-Order Differential Equations

This paper deals with two types of systems second-order differential equations parameters: coupled the boundary conditions Sturm–Liouville type and classical Dirichlet conditions. We discuss an Ambosetti–Prodi alternative for each system. For first system, we present sufficient existence non-existence its solutions, second a multiplicity solutions. Our arguments apply lower upper solutions method together properties Leary–Schauder topological degree theory. To best our knowledge, study is time that Ambrosetti–Prodi has been obtained such different parameters.