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 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.

Existence and Multiplicity of Positive Solutions for a Singular Third-Order Three-Point Boundary Value Problem with a Parameter

In this paper, we investigate the existence of positive solutions for a singular third-order three-point boundary value problem with a parameter. By using fixed point index theory, some existence, multiplicity and nonexistence results for positive solutions are derived in terms of different values of λ.

EXISTENCE OF POSITIVE SOLUTIONS TO A SINGULAR THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type,we establish results on the existence of at least one, at least two, and n positive solutions to the boundary value problem. Finally we give an example.

The Existence and Multiplicity of Positive Solutions for a Third-order Three-point Boundary Value Problem

Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.

EXISTENCE OF SOLUTIONS TO A THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.

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 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.

NONTRIVIAL SOLUTION OF A NONLINEAR SECOND-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.

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.

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.

Symmetric Positive Solutions of Nonlinear Singular Second-order Three-point Boundary Value Problem

In this paper, the second-order three-point boundary value problem u(t) + λa(t)f(t, u(t)) = 0, 0 < t < 1,u(t) = u(1- t), u(0)- u(1) = u(12)is studied, where λ is a positive parameter, under various assumption on a and f, we establish intervals of the parameter λ, which yield the existence of positive solution, our proof based on Krasnosel'skii fixed-point theorem in cone.{u"(t)+λa(t)f(t,u(t))=0,0<t<1,u(t)=u(1-t),u′(0)-u′(1)=u(1/2)is studied,where A is a positive parameter,under various assumption on a and f,we establish intervals of the parameter A,which yield the existence of positive solution,our proof based on Krasnosel'skii fixed-point theorem in cone.

POSITIVE SOLUTIONS OF THREE-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER DIFFERENTIAL EQUATIONS WITH AN ADVANCED ARGUMENT

By using the Krasnoselskii's fixed point theorem for cones,conditions for the existence of positive solutions to the three-point boundary value problem for second order differential equation with an advanced argumentu″(t)+λa(t)f(u(h(t)))=0, t∈(0,1), u(0)=0, αu(η)=u(1),where 0<η<1,0<α<1η and t≤h(t)≤1 are obtained.

Singular perturbation of a second-order three-point boundary value problem for nonlinear systems

This paper deals with the existence of solutions to a singularly perturbed second-order three-point boundary value problem for nonlinear differential systems. The authors construct an appropriate generalized lower- and upper-solution pair, a concept defined in this paper, and employ the Nagumo conditions and algebraic boundary layer functions to ensure the existence of solutions of the problem. The uniformly valid asymptotic estimate of the solutions is given as well. The differential systems have nonlinear dependence on all order derivatives of the unknown.

Monotone positive solution for three-point boundary value problem

In this paper, the existence of monotone positive solution for the following secondorder three-point boundary value problem is studied：x″（t）＋f（t,x（t））=0,0〈t〈1,x′（0）=0,x（1）＋δx′（η）=0,where η ∈ （0, 1）, δ∈ [0, ∞）, f ∈ C（[0, 1] × [0, ∞）, [0, ∞））. Under certain growth conditions on the nonlinear term f and by using a fixed point theorem of cone expansion and compression of functional type due to Avery, Anderson and Krueger, sufficient conditions for the existence of monotone positive solution are obtained and the bounds of solution are given. At last, an example is given to illustrate the result of the paper.

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.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR NONLINEAR THIRD-ORDER ROBIN BOUNDARY VALUE PROBLEM WITH A TURNING POINT

The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear thirdorder Robin boundary value problem with a turning point. In order to achieve this aim, existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions. In this manner, the goal of this paper is gained by applying the existence and uniqueness results mentioned above.