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An existence principle for boundary value problems for second order functional differential equations. (English) Zbl 0774.34052

The authors apply the topological transversality method of Granas to boundary value problems (BVP) for second order functional differential equations. They state a general existence principle for a BVP for functional differential equations by assuming a priori bounds on solutions and their derivatives. This assumption allows to omit the assumption (conventional for such problems) that the appearance function maps bounded sets of its domain, into bounded sets in its range. As applications of this existence principle a well-known theorem and a new result are stated in this paper.

MSC:

34K10 Boundary value problems for functional-differential equations
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