Boundary value problems for systems of second-order functional differential equations

S. Stanek, Department of Mathematics, Olomouc, Czech Republic

E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ., No. 28. (2000), pp. 1-14.

Abstract: Systems of second-order functional differential equations $(x'(t)+L(x)(t))'=F(x)(t)$ together with nonlinear functional boundary conditions are considered. Here $L:C^1([0,T];\R^n) \rightarrow C^0([0,T];\R^n)$ and $F:C^1([0,T];\R^n) \rightarrow L_1([0,T];\R^n)$ 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 conditions.

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