Existence of solution for m-point boundary value problems of second-order differential systems with impulses

摘要

With the help of the coincidence degree continuation theorem, we get a general theorem concerning the existence of solution of the m-point boundary value problems for second-order differential systems with impulses. We also give a definition of autonomous curvature bound set relative to this m-point boundary value problems, and by using this definition and the above existence theorem, we obtain some simple existence conditions of solution for these boundary value problems. In particular, when the impulses are absent, our results can be applied to study the usual m-point boundary value problems at resonance.