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
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 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
For most hierarchical triple stars, the classical double two-body model of zeroth-order cannot describe the motions of the components under the current observational accuracy. In this paper, Marchal＇s first-order ana...For most hierarchical triple stars, the classical double two-body model of zeroth-order cannot describe the motions of the components under the current observational accuracy. In this paper, Marchal＇s first-order analytical solution is implemented and a more efficient simplified version is applied to real triple stars. The results show that, for most triple stars, the proposed first-order model is preferable to the zerothorder model both in fitting observational data and in predicting component positions.展开更多
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 "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 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.
基金supported by the National Natural Science Foundation of China under Grant Nos. 11178006 and 11203086
文摘For most hierarchical triple stars, the classical double two-body model of zeroth-order cannot describe the motions of the components under the current observational accuracy. In this paper, Marchal＇s first-order analytical solution is implemented and a more efficient simplified version is applied to real triple stars. The results show that, for most triple stars, the proposed first-order model is preferable to the zerothorder model both in fitting observational data and in predicting component positions.
