On the correctness of nonlinear boundary value problems for systems of generalized ordinary differential equations
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The concept of a strongly isolated solution of the nonlinear boundary value problem
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 .
$$dx(t) = dA(t) \cdot f(t,x(t)),h(x) = 0,$$
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 Classification34B15
Key words and phrasesStrongly isolated solution correct problem Carathéodory class Opial condition
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