We consider the second-order differential equationu＂（t） ＋ q（t）f（t,u（t）,u＇（t）） =0, 0 〈 t 〈 1,subject to three-point boundry conditionu（0）=0, u（1） = aou（ζ0）,or to m-point boundary condition u＇（0...We consider the second-order differential equationu＂（t） ＋ q（t）f（t,u（t）,u＇（t）） =0, 0 〈 t 〈 1,subject to three-point boundry conditionu（0）=0, u（1） = aou（ζ0）,or to m-point boundary condition u＇（0）=m-2∑i=1biu]（ζi）,u（1）=m-2∑i=1aiu（ζi）.We show the existence of at least three positive solutions of the above multi-point boundary-value problem by applying a new fixed-point theorem introduced by Avery and Peterson.展开更多
This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t） ＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u）...This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t） ＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u） is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett-Williams and Krasnosel＇skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.展开更多
基金Supported by the "Qing-Lan" Project of Jiangsu Education Committeethe Natural Science Foundation of Jiangsu Education Committee (Grant No. 02KJD460011)
文摘We consider the second-order differential equationu＂（t） ＋ q（t）f（t,u（t）,u＇（t）） =0, 0 〈 t 〈 1,subject to three-point boundry conditionu（0）=0, u（1） = aou（ζ0）,or to m-point boundary condition u＇（0）=m-2∑i=1biu]（ζi）,u（1）=m-2∑i=1aiu（ζi）.We show the existence of at least three positive solutions of the above multi-point boundary-value problem by applying a new fixed-point theorem introduced by Avery and Peterson.
基金Supported by National Natural Science Foundation of China(Grant No.11071109)
文摘This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t） ＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u） is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett-Williams and Krasnosel＇skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.
