Non-negative solutions of systems of ODEs with coupled boundary conditions

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Solutions of perturbed Hammerstein integral equations with applications (2016, methodology): “leaves the cone K invariant and is compact, see for example Lemma 1 of [35].”
Multiple nonnegative solutions of systems with coupled nonlinear boundary conditions (2013, methodology): “The proof is omitted as it follows from the previous proof, for details see [21, 22].”