## Differential and Integral Equations

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

### On the nonautonomous higher-order Cauchy problems

#### 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