Differential and Integral Equations

On the nonautonomous higher-order Cauchy problems

Nguyen thanh Lan

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We study the existence and uniqueness of classical solutions to the following nonautonomous higher-order Cauchy problem, \begin{equation*} \begin{cases} u^{(n+1)}(t)= A(t)u^{(n)}(t)+B_1(t)u^{(n-1)}(t) \\ \hspace{45pt} + \cdots +B_n(t)u(t)+f(t), \ \ \ \ 0 \le s \le t \le T, \\ u^{(i)}(0)=x_{i} \in E , \hspace{4pt} i=0,1,\dots, n, \end{cases} \end{equation*} by using operator matrices. The results cover some of the known results about the existence and uniqueness of the higher-order Cauchy problem. An example and applications are also given.

Article information

Differential Integral Equations, Volume 14, Number 2 (2001), 241-256.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G10: Linear equations [See also 47D06, 47D09]
Secondary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]


Nguyen thanh Lan. On the nonautonomous higher-order Cauchy problems. Differential Integral Equations 14 (2001), no. 2, 241--256. https://projecteuclid.org/euclid.die/1356123355

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