一类非连续函数积分不等式中未知函数的估计及其应用.pdfVIP

2010,30A(4):1176–1182 ∗ 1,2 1 2,3  (1 546300; 2 550025; 3 )  [8]  - ÆÆÆ MR(2000) 34B15; 26D15 O178 A 1003-3998(2010)04-1176-07 1  1919 Gronwall[7] 0 ≤ u(t) ≤ t [bu(s) + a]ds, t ∈ [α, β], α a b 0 ≤ u(t) ≤ ahebh , t ∈ [α, β]. Bellman 1943 [3] u(t) ≤ c + t f (s)u(s)ds, t ∈ [α, β]. α t u(t) ≤ c exp α f (s)ds , t ∈ [α, β]. Gronwall-Bellman Æ Gronwall Bellman Gronwall-Bellman [3,7] ( ℄2009-06-07; 2010-07-29 E-mail: luoricai@163.com; wang4896@126.com; hongleix@ ∗ Æ℄ ℄ (200991265) ( [2007]34 ) (200707MS112) ([2008]2252) No.4  1177 [2, 10, 14], [1, 5, 9, 15–19]). Gronwall u(t) ≤ a + t f (s)w(u(s))ds + b(t) g (s)w(u(s))ds, t ≤ t t . 0 1 t0 b(t0) [1] Agarwal, Deng n bi (t) u(t) ≤ a(t) + g (t, s)w (u(s))ds, t ≤ t t . i i 0 1 i=1 bi (t0) Gronwall [12] 1957 y′′ + A(t)y = 0 2 2 t u (t) ≤ a + 2 f (s)u(s)ds, ∀t ≥ 0. (1.1) 0 (1.1) Pachpatte [13] 2 2 t u (t) ≤ a + 2 {f (s)u(s) + g (s)u(s)w