Singular Three-point Boundary Value Research Articles

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

This paper is concerned with the following second-order three-point boundary value problemu″t+β2ut+λqtft,ut=0,t∈0 , 1,u0=0,u(1)=δu(η), whereβ∈(0,π/2),δ>0,η∈(0,1), andλis a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and then some useful properties of Green’s function are obtained. Finally, existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values ofλby means of the fixed point index theory.

Eigenvalue for a singular second order three-point boundary value problem

In this paper, the existence of positive solutions for a singular second-order three-point boundary value problem is investigated. By using Krasnoselskii’s fixed point theorem, several sufficient conditions for the existence of positive solutions and the eigenvalue intervals on which there exist positive solutions are obtained. Finally, two examples are given to illustrate the importance of results obtained.

Positive solutions to singular third-order three-point boundary value problems on time scales

In this paper, we are concerned with singular third-order three-point boundary value problems on time scales. Some theorems on the existence of positive solutions are obtained by utilizing the fixed point theorem of cone expansion and compression type. An example is also given to illustrate our results.

Green's function and positive solutions of a singular nth-order three-point boundary value problem on time scales

In this paper, we investigate the existence of positive solutions for a class of singular nth-order three-point boundary value problem. The associated Green’s function for the boundary value problem is given at first, and some useful properties of the Green’s function are obtained. The main tool is fixed-point index theory. The results obtained in this paper essentially improve and generalize some well-known results.

Positive solutions for three-point semipositone boundary value problems with convex nonlinearity

In this paper, we consider the existence of positive solutions for a class of singular three-point semipositone boundary value problems with convex nonlinearity. By employing a well-known fixed point theorem, some new existence results are given under the case where nonlinearity can be sign-changing and have finitely many singularities.

Positive solutions to a singular second order three-point boundary value problem

A fixed point theorem is used to study a singular second order three-point boundary value problem. The problem is more general. Combining the method of constructing Green functions with operators defined piecewise, the existence resultof positive solutions to a singular second order three-point boundary value problem is established. The nonlinearity can be allowed to change sign.