二阶三点边值问题正解.pdfVIP

2008,28A(2):373–382 ∗ ℄ ( 030024) ′′ ′ −u (t) = b(t)f (u(t)) u (0) = 0, u(1) = αu(η) α, η ∈ (0, 1), f ∈ C ([0, ∞), [0, ∞)), b ∈ C ([0, 1], [0, ∞)) t ∈ [0, 1] b(t ) 0. ℄ Green Æ Hammerstein  0 0 ℄   MR(2000) 34B15 O175.8 A 1003-3998(2008)02-373-10 1   −u′′ (t) = b(t)f (u(t)), 0≤t≤1, (1) ′  u (0) = 0, u(1) = αu(η) α, η ∈ (0, 1), f ∈ C [0, ∞), [0, ∞) , b ∈ C [0, 1], [0, ∞) t ∈ [0, 1] b(t ) 0. Leray-Schauder 0 0 ( [1–6]), Liu[7] Krasnoselekii (1) [7] Green Hammerstein [7] ( 3.1). Hammerstein 2005-12-30; 2007-03-10 E-mail: zwangshuli@ ∗ 374 Vol.28A 2 Banach E = C [0, 1] , u = max |u(t)|. 0≤t≤1 r 0, E {u ∈ E : u r} Ω , Ω ∂Ω Ω r r r r 2.1 (1) C2 [0, 1] Hammerstein u(t) = 01 G(t, s)b(s)f (u(s))ds, 0 ≤ t ≤ 1 (2) E G(t, s) Green 1 − αη   − s, 0≤t≤s, 0≤s≤η,   1 − α