Differential and Integral Equations

On the nonautonomous higher-order Cauchy problems

Nguyen thanh Lan

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356123355

Mathematical Reviews number (MathSciNet)
MR1797389

Zentralblatt MATH identifier
1025.34051

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

Citation

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


Export citation