zbMATH — the first resource for mathematics

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

34B15 Nonlinear boundary value problems for ordinary differential equations
Full Text: DOI
[1] Bebernes, J.W; Schmitt, K, Periodic boundary value problems for systems of second order differential equations, J. differential equations, 13, 32-47, (1973) · Zbl 0253.34020
[2] Bernfeld, S; Lakshmikantham, V, An introduction to nonlinear boundary value problem, (1974), Academic Press New York/London · Zbl 0286.34018
[3] Cesari, L, Functional analysis and periodic solutions of nonlinear differential equations, Contrib. differential equations, 1, 149-167, (1963) · Zbl 0132.07101
[4] Knobloch, H.W, On the existence of periodic solutions of second order vector differential equations, J. differential equations, 9, 67-85, (1971) · Zbl 0211.11801
[5] Krasnosel’skii, M.A, ()
[6] Lloyd, N.G, Degree theory, (1978), Cambridge Univ. Press London · Zbl 0367.47001
[7] Mawhin, J, Topological degree methods in nonlinear boundary value problems, () · Zbl 0414.34025
[8] Schmitt, K, Periodic solutions of systems of second order differential equations, J. differential equations, 11, 180-192, (1972) · Zbl 0228.34023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.