Question

Consider the following initial value problem u'=A(x) u+ b(x), u(0)=u0

where A(x) is an n*n matrix and b(x) is an n-column vector

Assume that A(x) and b(x) are continuous on [0, infinity) ,and

0intinf || A(t) || dt < infinity, 0intinf || b(t) || dt < infinity

Prove that the solution u(x) is bounded on [0, infinity) with the following bound:

|| u(x) || <= [ || u0 || + 0intinf || b(t) || dt ] exp ( 0intinf || A(t) || dt ), 0<= x < infinity

Answer 1

note:
0intinf means integral from 0 to infinity

Answer 2

@oldrin.bataku please help me with this if you can

Answer 3

help please

Answer 4

(͡° ͜ʖ ͡°)

Answer 5

???!!!