On abstract nonlocal Cauchy problem

Adam Bednarz,

Ludwik Byszewski

Abstrakt

In this paper, we investigate the existence and uniqueness of the classical solution to an abstract
nonlocal Cauchy problem. For this purpose, we apply a notion of mild solution and the Banach
contraction theorem.

Słowa kluczowe: abstract Cauchy problem, nonlocal conditions, mild and classical solution
References

Byszewski L., Lakshmikantham V., Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Applic. Analysis 40, 1990, 11-19.

Byszewski L., Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem, J. of Appl. Math. and Stoch. Anal. 12.1, 1999, 91-97.

Kołodziej W., Mathematical Analysis, PWN, Warszawa 1978 (in Polish).

Lakshmikantham V., Leela S., Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, Oxford, New York, Paris 1981.