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Solvability of boundary value problems for vector differential systems*

Published online by Cambridge University Press:  14 November 2011

L. H. Erbe ,
Xinzhi Liu  and
Jianhong Wu
L. H. Erbe
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
Xinzhi Liu
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
Jianhong Wu
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
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Synopsis

Brouwer topological degree theory, the shooting type method, the disconjugacy theory of Hamiltonian systems and the Liapunov-Razumikhin technique of Volterra integrodifferential equations are employed to establish some solvability results for the 2n-dimensional differential system

subject to one of the following boundary conditions:

(i) x(0) = Qx(l), Qg(l x(1), qy(1)= g(0, x(0), y(0)),

(ii) Blx(O) = B2g(O, x(O), y(O)), C1x(l) = −C2g(l, x(l), y(l)),

where Q, Bi, Ci, i = 1, 2, are n x n real matrices. An application is given to the second order equation xn = h(t, x, x') subject to certain nonlinear boundary conditions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 3-4 , 1990 , pp. 181 - 193
Copyright
Copyright © Royal Society of Edinburgh 1990

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