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In this paper we present sufficient conditions for the existence ofheteroclinic or homoclinic solutions for second order coupled systems ofdifferential equations on the real line. We point out that it is required onlyconditions on the homeomorphisms and no growth or asymptotic conditions areassumed on the nonlinearities. The arguments make use of the fixed pointtheory, L^1-Carath\'eodory functions and Schauder's fixed point theorem. Anapplication to a family of second order nonlinear coupled systems of twodegrees of freedom, shows the applicability of the main theorem.

Heteroclinic and homoclinic solutions for nonlinear second-order coupled systems with phi-Laplacians