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Non-negative solutions of systems of ODEs with coupled boundary conditions. (English) Zbl 1280.34026
In this very well written and interesting paper, the authors study a coupled system of perturbed Hammerstein integral equations. Due to the generality of the system, the authors use it to study the existence of positive solutions of nonlocal boundary value problems for ordinary differential equations. In particular, the boundary conditions can be quite general, being as they are realized as Stieltjes integrals with positive measures. The technique used to study the problem is the classical fixed point index. The paper concludes with an illustrative example, which greatly assists the reader in appreciating the application and strength of the results stated in the paper. Any researcher interested in boundary value problems will find this paper to be of significant interest to him or her.

MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47H11 Degree theory for nonlinear operators
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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