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Existence of solutions to quasilinear differential equations in a Banach space
Published online by Cambridge University Press: 17 April 2009
Abstract
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