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
给出了FMP的三I解的一般形式 ,证明了关于区间值模糊推理的单调性定理、下确界定理以及存在性定理 .在分析了规则后件相对于前件的敏感性的基础上提出了 p 敏感参数概念 ,从而定义了 p 综合距离与 ( p θ)相对激活度 .将关于区间值模糊...给出了FMP的三I解的一般形式 ,证明了关于区间值模糊推理的单调性定理、下确界定理以及存在性定理 .在分析了规则后件相对于前件的敏感性的基础上提出了 p 敏感参数概念 ,从而定义了 p 综合距离与 ( p θ)相对激活度 .将关于区间值模糊推理的FOOL方法细致化为 ( p θ)算法 。展开更多
This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condit...This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.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.
基金Supported by the NNSF of China(10371006) Tianyuan Youth Grant of China(10626033).
文摘This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.
