Asymptotic formulas for the solutions of a system of linear differential equations $y^{\prime } = [A+B(x)]y$

Miloš Ráb

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On the representation of trajectories of bilinear systems and its applications

Sergej Čelikovský (1987)

Kybernetika

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Convolution in ${(W_{M, a}^{p})}^{'}$ -space

R. S. Pathak, S. K. Upadhyay (1997)

Rendiconti del Seminario Matematico della Università di Padova

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Beurling-Gevrey tempered ultradistributions as boundary values

Pilipovic, Stevan (1991)

Portugaliae mathematica

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Maximal estimates for nonsymmetric semigroups

Jacek Zienkiewicz (1994)

Studia Mathematica

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Characteristic Cauchy problems and solutions of formal power series

Sunao Ouchi (1983)

Annales de l'institut Fourier

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Let $L (z, \partial_{z}) = (\partial_{z_{0}})^{k} - A (z, \partial_{z})$ be a linear partial differential operator with holomorphic coefficients, where $A (z, \partial_{z}) = \sum_{j = 0}^{k - 1} A_{j} (z, \partial_{z^{'}}) (\partial_{z_{0}})^{j}, ord . A (z, \partial_{z}) = m > k$ and $z = (z_{0}, z^{'}) \in C^{n + 1} .$ We consider Cauchy problem with holomorphic data $L (z, \partial_{z}) u (z) = f (z), (\partial_{z_{0}})^{i} u (0, z^{'}) = {\hat{u}}_{i} (z^{'}) (0 \leq i \leq k - 1) .$ We can easily get a formal solution $\hat{u} (z) = \sum_{n = 0}^{\infty} {\hat{u}}_{n} (z^{'}) (z_{0})^{n} / n!$ , bu in general it diverges. We show under some conditions that for any sector $S$ with the opening less that a constant determined by $L (z, \partial_{z})$ , there is a function $u_{S} (z)$ holomorphic except on ${z_{0} = 0}$ such that $L (z, \partial_{z}) u_{S} (z) = f (z)$ and $u_{S} (z) \sim \hat{u} (z)$ as $z_{0} \to 0$ in $S$ .

Solving a class of generalized Lyapunov operator differential equations without the exponential operator function.

Lucas A. Jódar Sánchez (1990)

Publicacions Matemàtiques

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In this paper a method for solving operator differential equations of the type X' = A + BX + XD; X(0) = C, avoiding the operator exponential function, is given. Results are applied to solve initial value problems related to Riccati type operator differential equations whose associated algebraic equation is solvable.

Displaying similar documents to “Asymptotic formulas for the solutions of a system of linear differential equations y ' = [ A + B ( x ) ] y ”

On the representation of trajectories of bilinear systems and its applications

Convolution in ( W M , a p ) ' -space

Beurling-Gevrey tempered ultradistributions as boundary values

Maximal estimates for nonsymmetric semigroups

Characteristic Cauchy problems and solutions of formal power series

Solving a class of generalized Lyapunov operator differential equations without the exponential operator function.

Displaying similar documents to “Asymptotic formulas for the solutions of a system of linear differential equations $y^{'} = [A + B (x)] y$ ”

Convolution in ${(W_{M, a}^{p})}^{'}$ -space