Displaying similar documents to “Asymptotic relationship between solutions of two linear differential systems”

Approximate properties of principal solutions of Volterra-type integrodifferential equations with infinite aftereffect

Yu. A. Ryabov (1995)

Mathematica Bohemica

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The integrodifferential system with aftereffect (“heredity” or “prehistory”) dx/dt=Ax+-t R(t,s)x(s,)ds, is considered; here ε is a positive small parameter, A is a constant n × n matrix, R ( t , s ) is the kernel of this system exponentially decreasing in norm as t → ∞ . It is proved, if matrix A and kernel R ( t , s ) satisfy some restrictions and ε does not exceed some bound ε * , then the n -dimensional set of the so-called principal two-sided solutions x ˜ ( t , ε ) approximates in asymptotic sense the infinite-dimensional...

Linear integral equations in the space of regulated functions

Milan Tvrdý (1998)

Mathematica Bohemica

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n this paper we investigate systems of linear integral equations in the space 𝔾 L n of n -vector valued functions which are regulated on the closed interval [ 0 , 1 ] (i.e. such that can have only discontinuities of the first kind in [ 0 , 1 ] ) and left-continuous in the corresponding open interval ( 0 , 1 ) . In particular, we are interested in systems of the form x(t) - A(t)x(0) - 01B(t,s)[d x(s)] = f(t), where f ∈ 𝔾 L n , the columns of the n × n -matrix valued function A belong to 𝔾 L n , the entries of B ( t , . ) have a bounded variation...