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Existence of solutions to quasilinear differential equations in a Banach space

Published online by Cambridge University Press:  17 April 2009

James R. Ward
James R. Ward
Affiliation:
Department of Mathematics, Pan American University, Edinburg, Texas, USA.
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Abstract

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Initial value problems of the form x′ + A(t, x)x = f(t, x), x(0) = a, t ≥ 0, are considered in a real, separable, reflexive Banach space. Results concerning the existence of solutions on (0, ∞) are given by considering linear systems of the form x′ + A(t, u(t))x = f(t, u(t)). Here u(t) belongs to a suitable function space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 3 , December 1976 , pp. 421 - 430
Copyright
Copyright © Australian Mathematical Society 1976

References

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