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Criteria for the existence and uniqueness of solutions to nonlinear boundary value problems for systems of generalized ordinary differential equations. (English. Russian original) Zbl 0884.34029
Differ. Equations 32, No. 4, 442-450 (1996); translation from Differ. Uravn. 32, No. 4, 441-449 (1996).
The paper deals with the nonlinear boundary value problem for the system of generalized ODEs \[ dx(t)= dA(t)\cdot f(t,x(t)),\quad h(x)=0, \] where \(A= (a_{ij})^h_{i,j=1}: [a,b]\to \mathbb{R}^{n\times n}\) is a matrix function of bounded variation, \(f=(f_i)^n_{i=1}: [a,b]\times\mathbb{R}^n\to \mathbb{R}^n\) is a vector function of the Carathéodory class, and \(h\) is a continuous operator acting in the space of vector functions of bounded variation in \(\mathbb{R}^n\). The author finds a few types of sufficient conditions for the existence and uniqueness of a solution to this problem.

34B15 Nonlinear boundary value problems for ordinary differential equations
34K05 General theory of functional-differential equations