Multiplicity results for second-order m-point boundary value problem

By using fixed-point theorems, some new results for multiplicity of positive solutions for a class of second-order m-point boundary value problem are obtained. The associated Green's function of the problem is also given.     

Existence of positive solutions for a system of second-order m-point BVPs with variable parameters

In this paper, we study the existence of positive solutions for a class of second-order nonlinear m-point boundary value problems of differential system. By using the fixed point theory of cone expansion and compression with norm type, we show the sufficient conditions for the existence results.     

Positive solutions for singular m-point boundary value problems with positive parameter

In this paper, some new existence results for positive solutions for a class of singular m-point boundary value problems with parameter be obtained.     

The iterative solutions of 2nth-order nonlinear multi-point boundary value problems

The aim of this paper is to investigate the existence of iterative solutions for a class of 2nth-order nonlinear multi-point boundary value problems. The multi-point boundary condition under consideration includes various commonly discussed boundary conditions, such as three- or four-point boundary condition, (n + 2)-point boundary condition and 2(n − m)-point boundary condition. The existence problem is based on the method of upper and lower solutions and its associated monotone iterative technique. A monotone iteration is developed so that the iterative sequence converges monotonically to a maximal solution or a minimal solution, depending on whether the initial iteration is an upper solution or a lower solution. Two examples are presented to illustrate the results.     

Existence of two solutions of m-point boundary value problem for second order dynamic equations on time scales

In this paper, by means of a new twin fixed-point theorem in a cone, the existence of at least two positive solutions of m-point boundary value problem for second order dynamic equations on time scales is considered.     

Triple positive solutions for a class of -point dynamic equations on time scales with -Laplacian

This paper deals with a class of second-order nonlinear m-point dynamic equation on time scales with one-dimensional p-Laplacian. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f is involved with the first-order delta derivative explicitly. Meanwhile, an example is worked out to demonstrate the main results.     

The existence of positive solutions for second-order multi-point BVPs with the first derivative

By using the fixed-point index theory, several theorems of existence of positive solutions for second-order m$m$-point boundary value problem with the first derivative are obtained, where the nonlinear term may be noncontinuous. An example illustrating the main results is given.     

Positive solutions of m-point boundary value problems

The second-order m-point boundary value problem

     

A necessary and sufficient condition for 2nth-order singular super-linear m-point boundary value problems

In this paper, we study the existence of positive solutions for singular super-linear m-point boundary value problems of 2nth-order ordinary differential equations. A necessary and sufficient condition for the existence of C2n−2[0,1] positive solutions as well as C2n−1[0,1] positive solutions is given by means of the fixed point theorems on cones.     

A generalization of the cone expansion and compression fixed point theorem and applications

The classical Krasnosel’skii fixed point theorem concerning cone compression and expansion of norm type is extended; in it the norm is replaced with some convex functional. As an application, the existence of positive solutions for the singular second-order m$m$-point boundary value problem is considered.     

Multiple positive solutions of singular second-order m-point boundary value problems

The existence of multiple positive solutions about the singular second-order m-point boundary value problem

     

Positive solutions for m-point boundary-value problems with one-dimensional p-Laplacian

In this paper, we investigate the existence of positive solutions for a classes of m-point boundary value problems with p-Laplacian. By applying a monotone iterative technique, some sufficient conditions for the existence of twin positive solutions are established.     

On the existence of positive solution for a kind of multi-point boundary value problem at resonance

This paper concerns the existence of positive solution for a class of second-order m-point boundary value problems under different resonant conditions. By using the Leggett-Williams norm-type theorem due to O’Regan and Zima, we obtain the existence of positive solution. An example is given to demonstrate the main results.     

Existence of positive solutions to n-point nonhomogeneous boundary value problem

In this paper, we are concerned with the existence of positive solutions to a n-point nonhomogeneous boundary value problem. By using the Krasnoselskii's fixed point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of positive solution is established for the n-point nonhomogeneous boundary value problem.     

The method of lower and upper solutions for fourth order singular m-point boundary value problems

This paper investigates the existence of positive solutions for fourth order singular m-point boundary value problems. Firstly, we establish a comparison theorem, then we define a partial ordering in C²[0,1]∩C⁴(0,1) and construct lower and upper solutions to give a necessary and sufficient condition for the existence of C²[0,1] as well as C³[0,1] positive solutions. Our nonlinearity f(t,x,y) may be singular at x, y, t=0 and/or t=1.     

Positive Solutions for a Higher-Order m-Point Boundary Value Problem

We study the existence of positive solutions for a higher-order nonlinear differential system subject to some m-point boundary conditions. As applications of the main results, we present two existence theorems for the positive solutions of a higher-order nonlinear differential equation with boundary conditions of the same form as those for the studied system.     

A generalization of the Leggett-Williams fixed point theorem and its application

A generalization of the Leggett-Williams fixed point theorem is established. As an application, the existence of multiple nondecreasing positive solutions for a class of third-order m-point boundary value problems is obtained.     

Nontrivial solutions of singular nonlinear m-point boundary value problems

In this paper, by using the method of topology degree, some existence theorems of nontrivial solutions for singular nonlinear m-point boundary value problems are established. Our nonlinearity may be singular in its dependent variable.     

An existence and uniqueness criterion for solutions of boundary value problems

In this paper a technique is developed for the study of the existence and uniqueness of solutions to nth order ordinary differential equations satisfying n-point boundary conditions. Liapunov-like functions are employed to determine the existence and uniqueness of solutions to linear equations satisfying the boundary conditions, and these solutions are in turn used to determine existence for the general nonlinear case. A by-product of this technique is a matching technique for linear equations by which solutions of certain k-point boundary value problems (k < n) can be matched to extend the interval of existence for solutions to the n-point problem.     

Existence of multiple positive solutions for nth-order p-Laplacian m-point singular boundary value problems

In this paper, by using fixed point theorem, we prove the existence of multiple positive solutions for a class of nth-order p-Laplacian m-point singular boundary value problem. The interesting point is that the nonlinear term f explicitly involves the each-order derivative of variable u(t).