The Existence of Solutions of Three-point Boundary Value Problems for Second Order Impulsive Differential Equation

We study the existence of solutions to the second order three-point boundary value problem：{x″（t）＋f（t,x（t）,x′（t））=0,t≠ti,△x（ti）=Ii（x（ti）,x′（ti））,i=1,2,…,k,△x′（ti）=Ji（x（ti）,x′（t））,i=1,2,…,k,x（0）=0=x（1）-αx（η）,where 0〈η〈1,α∈R,and f：[0,1]×R×R→R,Ii：R×R→R,Ji：R×R→R（i=1,2,…,k）are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.

TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem： -u′′（t） = λf（t, u（t）） for all t ∈ （0, 1） subjecting to u（0） = 0 and αu（η） = u（1）, where η ∈ （0, 1）, α ∈ [0, 1）, and λ is a positive parameter. The nonlinear term f（t, u） is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ＊ ∈ （0, ＋∞], such that the above problem has at least two positive solutions for any λ ∈ （0, λ＊） under certain conditions on the nonlinear term f.

Existence of Multiple Positive Solutions for Second-order Three-point Boundary Value Problems on a Half-line

In this paper,we are concerned with the existence of multiple positive solutions to a second-order three-point boundary value problem on the half-line.The results are obtained by the Leggett-Williams fixed point theorem.

Positive solutions of three-point boundary value problems

In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian. We then study existence of solutions when the problems are in resonance cases. The proposed approach is based on the Krasnoselskii＇s fixed point theorem and the coincidence degree.

Existence of Sign-changing Solution for Three-point Boundary Value Problems

In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.

Solvability of Third-order Three-point Boundary Value Problems with Caratheodory Nonlinearity

A class of third-order three-point boundary value problems is considered, where the nonlinear term is a Caratheodory function. By introducing a height function and considering the imtegration of this height function, an existence theorem of solution is proved when the limit growth function exists. The main tools are the Lebesgue dominated convergence theorem and the Schauder fixed point theorem.

A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems

Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.

The Existence and Uniqueness of Positive Solutions for a Singular Nonlinear Three-Point Boundary Value Problems

Using the method of lower and upper solutions, we study the following singular nonlinear three-point boundary value problems: , where K ∈ C[0,1] ,0 α η < 1 and λ is a positive parameter and present the existence, uniqueness, and the dependency on parameters of the positive solutions under various assumptions. Our result improves those in the previous literatures.

SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY

In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.

EXISTENCE THEOREMS FOR A SECOND ORDER THREE-POINT BOUNDARY VALUE PROBLEM WITH IMPULSES

In this paper,two existence theorems are given concerning the following 3-point boundary value problem of second order differential systems with impulses[HL(2:1,1Z;2,1Z]x″(t)=f(t,x(t),x′(t)),t∈(0,1),t≠t_k,k=1,2,...,m, Δx|_~t=t_k =I_k(x(t_k)),k=1,2,...,m, Δx′|_~t=t_k =J_k(x(t_k),x′(t_k)),k=1,2,...,m, x(0)=0,x(1)=αx(η).

Existence of solutions of nonlinear two-point boundary value problems for 4nth-order nonlinear differential equation

Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear 4n-th-order differential equationy (4n)=f(t,y,y′,y″,...,y (4n-1))(a)with the boundary conditions g 2i(y (2i)(a),y (2i+1)(a))=0,h 2i(y (2i)(c),y (2i+1)(c))=0,(i=0,1,...,2n-1)(b) where the functions f, g i and h i are continuous with certain monotone properties. For the boundary value problems of nonlinear nth order differential equationy (n)=f(t,y,y′,y″,...,y (n-1))many results have been given at the present time. But the existence of solutions of boundary value problem (a),(b) studied in this paper has not been covered by the above researches. Moreover, the corollary of the important theorem in this paper, i.e. existence of solutions of the boundary value problem.y (4n)=f(t,y,y′,y″,...,y (4n-1)) a 2iy (2i)(a)+a 2i+1y (2i+1)(a)=b 2i,c 2iy (2i)(c)+c 2i+1y (2i+1)(c)=d 2i,(i=0,1,...2n-1)has not been dealt with in previous works.

Existence of Positive Solutions of Three-point Boundary Value Problem for Higher Order Nonlinear Fractional Differential Equations

In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.

Precise integration method for a class of singular two-point boundary value problems

In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.

Existence of Multiple Positive Solutions for Third-Order Three-Point Boundary Value Problem

In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.

Triple Positive Solutions to a Third-order Three-point Boundary Value Problem with p-Laplacian Operator

In this paper, we consider the three-point boundary value problem （φp（uˊˊ（t）））ˊ ＋a（t）f（t, u（t）, uˊ（t）, uˊˊ（t）） = 0, t ∈ [0, 1] subject to the boundary conditions u（0） =βuˊ（0）, uˊ（1） = αuˊ（η）, uˊˊ（0） = 0, where φp（s） = ｜s｜p？2s with p 〉 1, 0 〈 α, η 〈 1 and 0 ≤ β 〈 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.

Positive Solutions for Fractional Differential Equations with Multi-Point Boundary Value Problems

In this paper, a fractional multi-point boundary value problem is considered. By using the fixed point index theory and Krein-Rutman theorem, some results on existence are obtained.

Positive Solutions of a Second-Order Three-point Boundary Value Problem

The existence of positive solutions is established for a nonlinear second-order three-point boundary value problem. The result improves and extends the main result in Electron J. Differential Equations, 34(1999), 1-8.

On the Existence of Positive Solution for a Nonlinear Third-order Three-point Boundary Value Problem

An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.

Existence of Two Solutions of Nonlinear m-Point Boundary Value Problems

Sufficient conditions for the existence of at least two positive solutions of a nonlinear m -points boundary value problems are established. The results are obtained by using a new fixed point theorem in cones. An example is provided to illustrate the theory.

Triple Positive Solutions for a Third-order Three-point Boundary Value Problem

In this paper,we study the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem ■where η∈[0,1/2) is a constant,by using a fixed-point theorem due to Avery and Peterson,we establish results of triple positive solutions to the boundary value problem,and an example is given to illustrate the importance of result obtained.