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Journal of the London Mathematical Society 1983 s2-27(1):121-129; doi:10.1112/jlms/s2-27.1.121
© 1983 by London Mathematical Society
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© Oxford University Press

On Existence, Uniqueness and Approximation of Solutions of Ordinary Differential Equations in Banach Spaces

M. Arrate and A. G. García

Sección de Matemáticas, Facultad de Ciencias, Universidad de Valladolid Valladolid, Spain

The problem of uniqueness and existence of solutions to the initial value problem x' = f(t, x), x(0) = x'o {varepsilon} E, where E is a Banach space, is considered. Dissipative type conditions are employed. Finally, Galerkin approximations of the solutions are treated.


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