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Boundary value problems for systems of second order differential equations

Published online by Cambridge University Press:  14 November 2011

L. H. Erbe  and
H. W. Knobloch
L. H. Erbe
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada
H. W. Knobloch
Affiliation:
Mathematisches Institut, Am Hubland, Würzburg, Federal, Republic of Germany
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Synopsis

We consider boundary value problems for second order differential systems of the form (1)x” = A(t)x′ + f(t, x) and (2) x” = A(t)x′ + f(t, x) + q(t, x). By assuming the existence of a solution to (1) with a given region in (t, x) space, we derive conditions under which there exists a solution to (2) which stays in a certain neighbourhood of and satisfies given boundary conditions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 1-2 , 1985 , pp. 61 - 76
Copyright
Copyright © Royal Society of Edinburgh 1985

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