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Boundary value problems for second-order differential systems. (English) Zbl 0635.34017
Sufficient conditions for the existence of a solution to the BVP \(x''=f(t,x,x')\), \(x(0)=Q_ 0x(1)\), \(x'(0)=Q_ 1x'(1)\) are obtained, where \(Q_ 0\), \(Q_ 1\) are non-singular \(n\times n\) matrices with \(Q_ 0\) orthogonal. The results obtained extend those for the periodic case obtained by J. W. Bebernes and K. Schmitt [J. Differ. Equations 13, 32-47 (1973; Zbl 0253.34020)] and are obtained by appropriate modifications of a Leray-Schauder degree argument.
Reviewer: L.Erbe

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
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