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Boundary value problems for systems of second-order functional differential equations. (English) Zbl 0971.34051
Summary: Systems of second-order functional-differential equations \[ (x^\prime(t)+L(x)(t))^\prime=F(x)(t) \] together with nonlinear functional boundary conditions are considered. Here, \[ L:C^1([0,T];\mathbb{R}^n) \rightarrow C^0([0,T];\mathbb{R}^n)\qquad\text{and}\qquad F:C^1([0,T];\mathbb{R}^n) \rightarrow L_1([0,T];\mathbb{R}^n) \] are continuous operators. Existence results are proved by the Leray-Schauder degree and the Borsuk antipodal theorem for \(\alpha\)-condensing operators. Examples demonstrate the optimality of the conditions.

MSC:
34K10 Boundary value problems for functional-differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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