On the correctness of linear boundary value problems for systems of generalized ordinary differential equations
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The sufficient conditions are established for the correctness of the linear boundary value problem
whereA:[a,b]→ℝn×n andf:[a,b]→ℝ n are matrix- and vectorfunctions of bounded variation,c0∈ℝ n , andl is a linear continuous operator from the space ofn-dimentional vector-functions of bounded variation into ℝ n .
$$dx(t) = dA(t) \cdot x(t) + df(t),l(x) = c_0 ,$$
1991 Mathematics Subject Classification34B05
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- 1.M.T. Ashordia, On the continuous dependence on the parameter of the solution of the Cauchy problem for a system of generalized ordinary differential equations. (Russian)Proc. I. Vekua Inst. Appl. Math. Tbiliss. State Univ. 31(1988), 5–22.Google Scholar
- 3.I.T. Kiguradze, Boundary value problems for systems of ordinary differential equations. (Russian)Current problems in mathematics. Newest results, v. 30, (Russian) 3–103,Itogi nauki i tekhniki, Akad. Nauk SSSR, Vsesoyuzn. Inst. Nauchn i Tekhnich. Inform., Moscow, 1987.Google Scholar
- 4.M.A. Krasnoselski and S.G. Krein, Averaging principle in nonlinear mechanics. (Russian),Uspekhi Mat. Nauk 10(1955), No. 3, 147–152.Google Scholar
- 6.S. Schwabik, M. Tvrdy and O. Vejvoda, Differential and integral equations: Boundary value problems and adjoints.Academia, Praha, 1979.Google Scholar
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