By Hugo. Rossi
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Extra info for Advanced calculus. Problems and applications to science and engineering
3 Let f be a nonnegative continuous function defined for t ~ R+, such that f o f (s) ds < oo and n(t) > 0 be a continuous and decreasing function defined for t ~ R+. 8) t then u(t) < n (t) exp ( ft f (s) ds ) , t 6 R+. 1 with suitable modifications. Rodrigues (1980) proved, and made use of, the following inequality to study the growth and decay of solutions of perturbed retarded linear equations. 4 Let f , g be nonnegative continuous functions defined for t ~ R+. Let y(t) > 0 be a decreasing continuous function, for t > cr and ~r sufficiently large, in such a way that fl-- foo g(s) ds + f oo f (s)ds < 1.
3) we have v'(t) 2 yields F(t) <_M exp ( ~ h(s) ds) . 5) and splitting we get f(t)
Advanced calculus. Problems and applications to science and engineering by Hugo. Rossi
2 yields F(t) <_M exp ( ~ h(s) ds) . 5) and splitting we get f(t)