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The Existence of Solutions to a Class of multi-point boundary value problem of Fractional Differential Equation

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Journal of Mathematical Research with Applications 2013年第2期33卷 175-188页

作者： Xiaohong HAO Zongfu ZHOU Department of Mathematical Sciences Anhui University

In this paper,we consider the following multi-point boundary value problem of fractional differential equation Dα0+u(t) = f(t,u(t),Dα 10+u(t),Dα 20+u(t),Dα 30+u(t)),t ∈(0,1),mI4 α0+u(0) = 0,Dα 10+u(0) =i=1αiDα 10+u(ξi),Dα 20+u(1) =nj=1βjDα 20+u(ηj),Dα 30+u(1) Dα 30+u(0) = Dα 20+u(12),where 3 < α≤ 4 is a real *** applying Mawhin coincidence degree theory and constructing suitable operators,some existence results of solutions can be established.

关键词： fractional differential equation multi-point boundary value problem coincidence degree.

multiple Positive Solutions for multi-point boundary value problem of Fractional Differential Equation

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Journal of Mathematical Research with Applications 2017年第2期37卷 223-232页

作者： Xiping LIU Mei JIA Ming NIU Xiufen XIANG College of Science University of Shanghai for Science and Technology Department of Mathematics and Physics Chengde Petroleum College Department of Mechanics and Electronics Shijiazhuang Vocational Technology Institute

In this paper, we study the multiplicity of positive solutions for multi-point boundary value problem of Riemann-Liouville fractional differential equation with multi-terms fractional derivative in the boundary conditions. By using the properties of the Green function and a generalization of the Leggett-Williams fixed point theorem due to the work of Bai and Ge, the sufficient conditions to guarantee the existence of at least three positive solutions are established. In the end of this paper, we have also given out the example to illustrate the wide range of potential application of our main results.

关键词： fractional differential equation multi-point boundary value problem positive solution Green function fixed point theorem

EXISTENCE OF TRIPLE POSITIVE SOLUTIONS TO A multi-point boundary value problem

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Annals of Differential Equations 2011年第2期27卷 201-206页

作者： Bo Sun (School of Applied Math., Central University of Finance and Economics, Beijing 100081) Aijun Yang (College of Science, Zhejiang University of Technology, Hangzhou 310032)

We apply a fixed point theorem to verify the existence of at least three positive solutions to a multi-point boundary value problem with p-Laplacian. Existence criteria which ensure the existence of triple positive so... 详细信息

关键词： positive solutions fixed point theorem multi-point boundary value problem p-Laplacian

Existence Results of Third Order multi-point boundary value problem at Resonance

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Journal of Beijing Institute of Technology 2005年第4期14卷 449-452页

作者：杜增吉白占兵葛渭高 School of Science Beijing Institute of Technology Beijing100081 China School of Science Beijing Institute of Technology Beijing100081 ChinaCollege of Information Science and Technology Shandong University of Science and Technology Qingdao266510 China

A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂（ t ）, x＇＇＇（ t ））＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0,... 详细信息

A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂（ t ）, x＇＇＇（ t ））＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0, 1]×R^3, e（t）∈L^1[0, 1],a≥0, is considered, all theβj＇s have not the same sign, 0〈ξ〈 l, 0〈η1〈 η2〈… 〈ηm.2〈 1. By using the coincidence degree theory, some existence theorems for the problems at resonance are obtained.

关键词： multi-point boundary value problem resonance coincidence degree theory

Solvability of multi-point boundary value problem

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Journal of Mathematical Research and Exposition 2009年第4期29卷 693-699页

作者：张慧星刘文斌张建军陈太勇 Department of Mathematics China University of Mining and Technology

This paper deals with the existence of solutions for the problem{（Фp（u′））′=f（t,u,u′）,t∈（0,1）, u′（0）=0,u（1）=∑i=1^n-2aiu（ηi）,where Фp（s）=｜s｜^p-2s,p〉1.0〈η1〈η2〈…〈ηn-2〈1,ai（i=1,2,…,n-2）are non-negative constants and ∑i=1^n-2ai=*** known results are improved under some sign and growth conditions. The proof is based on the Brouwer degree theory.

关键词： p-Laplace multi-point boundary value problem resonance degree theory.

multi-point boundary value problems for Nonlinear Fourth-order Differential Equations with All Order Derivatives

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Communications in Mathematical Research 2013年第2期29卷 108-120页

作者： Yang Liu Shi Shao-yun Department of Mathematics Hefei Normal University

By using fixed point theorem, multiple positive solutions for some fourth- order multi-point boundary value problems with nonlinearity depending on all order derivatives are obtained. The associated Green＇s functions... 详细信息

关键词： multi-point boundary value problem positive solution cone fixed point

SOLVABILITY FOR SECOND-ORDER multi-point boundary value problemS ON A HALF-LINE

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Annals of Differential Equations 2012年第2期28卷 157-163页

作者： Yu Duan, Hairong Lian, Xin Yu (School of Sciences, China University of Geosciences, Beijing 100083)

In this paper, we are concerned with the existence of a second-order differential equation with m-point boundary conditions on the half line. The existence results are proved by the Leray-Scha¨uder point theorem in a special Banach space. Green function plays an important role in the proof and its discussion is very interesting. The results obtained generalize those in the previous references.

关键词： multi-point boundary value problem Green function Leray-Scha¨uder fixed point theorem half-line

Solvability of 2n-order m-point boundary value problem at resonance

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Applied Mathematics and Mechanics(English Edition) 2007年第9期28卷 1219-1226页

作者：江卫华郭彦平仇计清 College of Mathematics and Science of Information Hebei Normal University College of Sciences Hebei University of Science and Technology

The existence of solutions at resonance is obtained by using the an example to demonstrate our result. noncontinuous. for the 2n-order m-point boundary value problem coincidence degree theory of Mawhin. We give The ... 详细信息

关键词： resonance Predholm operator multi-point boundary value problem coincidence degree theory

Positive Solutions of a Weak Semipositone Third-Order Three-point boundary value problem

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Journal of Mathematical Research and Exposition 2010年第1期30卷 173-180页

作者： Qing Liu YAO Department of Applied Mathematics Nanjing University of Finance and Economics Jiangsu 210003 P. R. China

The positive solutions are studied for the nonlinear third-order three-point boundary value problem u′″（t）=f（t,u（t））,a.e,t∈[0,1],u（0）=u′（η）=u″（1）=0, where the nonlinear term f（t, u） is a Caratheodory function and there exists a nonnegative function h ∈ L^1[0, 1] such that f（t, u）〉 ≥-h（t）. The existence of n positive solutions is proved by considering the integrations of ＂height functions＂ and applying the Krasnosel＇skii fixed point theorem on cone.

关键词： singular ordinary differential equation multi-point boundary value problem posi-tive solution existence multiplicity.