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Criteria of correctness of linear boundary value problems for systems of generalized ordinary differential equations. (English) Zbl 0879.34037
For generalized linear differential equations of the form \[ dx(t)=dA_k(t).x(t) +df_k(t) \] with abstract side conditions \(l_k(x)=c_k\), where \(l_k:BV_n(a,b)\to \mathbb{R}^n\) is a sequence of bounded linear operators, \(c_k\in \mathbb{R}^n\), conditions are given such that the sequence of solutions \(x_k\) of the boundary value problem converges uniformly to the solution of the limiting problem \(dx(t)=dA_0(t).x(t) +df_0(t)\) with the side condition \(l_0(x)=c_0\).

MSC:
34B99 Boundary value problems for ordinary differential equations
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References:
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