Abstract
We shall give the necessary and sufficient condition for the existence of the homoclinic orbit of the planar system including generalized Lienard-type systems. Our idea is to apply curves with some invariance to the existence of the homoclinic orbit of the system. It shall be shown that the positions of these curves on the phase space play an important role in the existence of homoclinic orbits of the system. The results will be applied to many examples.
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