Asymptotic relationship between solutions of two linear differential systems

Jozef Miklo

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 $n \times n$ matrix, $R (t, s)$ is the kernel of this system exponentially decreasing in norm as $t \to \infty$ . 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 $\tilde{x} (t, ε)$ 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 $f \in 𝔾_{L}^{n}$ , the columns of the $n \times n$ -matrix valued function $A$ belong to $𝔾_{L}^{n}$ , the entries of $B (t, .)$ have a bounded variation...

Upper and lower solutions for singularly perturbed semilinear Neumann's problem

Róbert Vrábeľ (1997)

Mathematica Bohemica

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The paper establishes sufficient conditions for the existence of solutions of Neumann’s problem for the differential equation $μ y " + k y = f (t, y)$ which tend to the solution of the reduced problem $k y = f (t, y)$ on $[0, 1]$ as $μ \to 0 .$

Existence of oscillatory and nonoscillatory solutions for a class of neutral functional differential equations

Y. Kitamura, Takaŝi Kusano, Bikkar S. Lalli (1995)

Mathematica Bohemica

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For a certain class of functional differential equations with perturbations conditions are given such that there exist solutions which converge to solutions of the equations without perturbation.