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Georgian Mathematical Journal

, Volume 3, Issue 5, pp 501–524 | Cite as

On the correctness of nonlinear boundary value problems for systems of generalized ordinary differential equations

  • M. Ashordia
Article

Abstract

The concept of a strongly isolated solution of the nonlinear boundary value problem
$$dx(t) = dA(t) \cdot f(t,x(t)),h(x) = 0,$$
is introduced, whereA: [a, b]→R n×n is a matrix-function of bounded variation,f: [a, b]×R n →R n is a vector-function belonging to a Carathéodory class, andh a continuous operator from the space ofn-dimensional vector-functions of bounded variation intoR n .

It is stated that the problems with strongly isolated solutions are correct. Sufficient conditions for the correctness of these problems are given.

1991 Mathematics Subject Classification

34B15 

Key words and phrases

Strongly isolated solution correct problem Carathéodory class Opial condition 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • M. Ashordia
    • 1
  1. 1.A. Razmadze Mathematical InstituteGeorgian Academy of SciencesTbilisiRepublic of Georgia

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