Abstract
The aim of this paper is to investigate the existence and uniqueness of a classical solution to a functional‐differential abstract nonlocal Cauchy problem in a general Banach space. For this purpose, a special kind of a mild solution is introduced and the Banach contraction theorem and a modified Picard method are applied.
Highlights
We present four theorems (Theorems 2.1-2.4) on the existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem in an arbitrary Banach space and give an approximation of the solution to the nonlocal problem
In the proofs of the theorems, we introduce a special kind of a mild solution and apply the Banach contraction theorem and a modified Picard method of successive approximations
The special kind of a mild solution in this paper is a modification of a mild solution introduced by the author, for nonlocal evolution problems
Summary
The aim of this paper is to investigate the existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem in a general Banach space. AMS subject classifications: 34G20, 34K30, 34A12, 34A34, 47H10, 34A45, 34G99
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