Abstract
The aim of the paper is to prove a theorem about the existence of an approximate solution to an abstract nonlinear nonlocal Cauchy problem in a Banach space. The right‐hand side of the nonlocal condition belongs to a locally closed subset of a Banach space. The paper is a continuation of papers [1], [2] and generalizes some results from [3].
Highlights
In papers [1] and [2], theorems about the existence and uniqueness of solutions of abstract nonlinear nonlocal Cauchy problems in Banach spaces were considered
The aim of this paper is to construct an approximate solution to an abstract nonlinear nonlocal Cauchy problem in a Banach space under the assumptions that the right-hand side of the differential equation does not satisfy any kind of the Lipschitz condition and under the assumption that the right-hand side of the nonlocal condition belongs to a locally closed subset of a Banach space
To prove the main result of the paper, a modification of a method used by Lakshmikantham and Leela is applied
Summary
150 West University Blvd. Melbourne, Florida 2901-6988, U.S.A. The aim of the paper is to prove a theorem about the existence of an approximate solution to an abstract nonlinear nonlocal Cauchy problem in a Banach space. The right-hand side of the nonlocal condition belongs to a locally closed subset of a Banach space. The paper is a continuation of papers [1], [2] and generalizes some results from [3]. Key words: Abstract nonlinear nonlocal Cauchy problem, locally closed sets, existence of an approximate solution. AMS (MOS) subject classifications: 34A45, 34A99, 34G20, 34G99.
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