A Variation of the Topological Method of Wazewski

A theorem of Wazewski type is proved for the existence of solutions of the vector system y' = f(t, y) without assuming that solutions of initial value problems are unique. The theorem is then used to prove the existence of solutions of certain types of boundary value problems for the equation x...

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Bibliographic Details
Published in:	SIAM journal on applied mathematics Vol. 20; no. 1; pp. 124 - 130
Main Authors:	Jackson, Lloyd K., Klaasen, Gene
Format:	Journal Article
Language:	English
Published:	Society for Industrial and Applied Mathematics 01-01-1971
Subjects:	Boundary value problems Cauchy problem Continuous functions Differential variability inequalities Existence theorems Topological theorems
Online Access:	Get full text
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Summary:	A theorem of Wazewski type is proved for the existence of solutions of the vector system y' = f(t, y) without assuming that solutions of initial value problems are unique. The theorem is then used to prove the existence of solutions of certain types of boundary value problems for the equation x" = h(t, x, x').
ISSN:	0036-1399 1095-712X
DOI:	10.1137/0120016