Theorem about the existence and uniqueness of a solution of a nonlocal abstract cauchy problem in a banach space

1991/01/01 by Ludwik Byszewski, V. Lakshmikantham · 1 citation
Mathematics · #Differential Equations and Boundary Problems #Nonlinear Differential Equations Analysis

paper · doi:10.1080/00036819008839989

crossref issued 1991/01/01 · crossref published 1991/01/01 · crossref published-print 1991/01/01 · openalex publication_date 1991/01/01 · crossref created 2007/06/25 · crossref deposited 2016/12/10 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31

Abstract

The aim of the paper is to give a theorem about the existence and uniqueness of a solution of a nonlocal Cauchy problem for an ordinary differential equation in a Banach space. The Banach theorem about the fixed point is used to prove the existence and uniqueness of a solution of the problem considered. The result obtained in this paper can be applied among other things to the description of motion phenomena with better effect than the classical Cauchy problem.

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