Solvability of second order coupled systems on the half-line

This work considers a second order coupled system of differential equations in semi-infinite intervals. The arguments apply the fixed point theory, Green’s functions technique, L1-Carathéodory functions theory, a truncature technique and Schauder’s fixed point theorem.
The technique used consists in to apply a Nagumo-type growth condition to nonlinearities, and the concept of equiconvergent to recover the compactness of the associated operators. Lastly, an application to a predator-prey model is presented.

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