Home /
Expert Answers /
Other Math /
gronwall-inequality-let-r-k-and-f-be-real-and-continuous-functions-which-satisfy-r-t-gt-0-k-t-pa221
(Solved): (Gronwall inequality) Let r,k, and f be real and continuous functions which satisfy r(t)>=0,k(t)& ...
(Gronwall inequality)
Let r,k, and f be real and continuous functions which satisfy r(t)>=0,k(t)>=0, and
r(t)<=f(t)+\int_a^t k(s)r(s)ds,a<=t<=b
Show that
r(t)<=\int_a^t f(s)k(s)exp[\int_s^t k(u)du]ds+f(t),a<=t<=b