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.

EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.

Existence Theory for Single and Multiple Positive Solutions to Singular Boundary Value Problems for Second-order Differential Systems P-Laplacian

In this paper we present some new existence results for singular boundary value problems by Arzela-Ascoli theorem. In particular our nonlinearity may be singular in its dependent variable.

Positive Solutions for Semipositone m-point Boundary-value Problems

Let ξ i ∈ (0, 1) with 0 < ξ1 < ξ2 < ··· < ξ m?2 < 1, a i , b i ∈ [0,∞) with and . We consider the m-point boundary-value problem

Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems

This paper is devoted to the study ofthe existence of single and multiple positive solutions for the first order boundary value problem x′= f（t, x）, x（0） = x（T）, where f ∈ C（[0,T] × R） . In addition, we apply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at the origin. Our proofs are based on a fixed point theorem in cones. Our results improve some recent results in the literatures.

Existence and finite-time stability of a unique almost periodic positive solution for fractional-order Lasota Wazewska red blood cell models

In this paper,we are concerned with a class of fractional-order Lasota-Wazewska red blood ccll modcls.By applying a fixed point theorem on a normal cone,we first obtain the sufficient conditions for the existence of a unique almost periodic positive solution of the considered models.Then,considering that all of the red blood cells in animals survive in a finite-time interval,we study the finite-time stability of the almost periodic positive solution by using some inequality techniques.Our results and methods of this paper are new.Finally,we give numerical examples to show the feasibility of the obtained results.

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO NONLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM

In this paper, we study a nonlinear semipositone Neumann boundary value problem. Under some suitable conditions, we prove the existence and multiplicity of positive solutions to the problem, based on Krasnosel’skii’s fixed point theorem in cones.

Multiplicity of Positive Solutions to Period Boundary Value Problems for Second Order Impulsive Differential Equations

This paper deals with the existence and multiplicity of positive solutions to second order period boundary value problems with impulse effects. The proof of our main results relies on a well-known fixed point theorem in cones. The paper extends some previous results and reports some new results about impulsive differential equations.

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO COHEN-GROSSBERG NEURAL NETWORKS WITH DELAYS ON TIME SCALES

By the time scales calculus theory and the Krasnoselskii fixed point theorem in cones, some sufficient conditions ensuring the existence of positive periodic solutions to a kind of Cohen-Grossberg neural networks on time scales with delays are obtained.