Abstract
The main purpose of this paper is to study homoclinic bifurcation in a degenerate case of differential equations of form x˙=f(x⋅ɛ) and x˙=g(x)+h(t,x⋅ɛ). By using theory of exponential dichotomies and Liapunov-Schmidt method, the authors obtain the Melnikov-like vectors by which the existence of homoclinic orbits can be detected.
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