Higher-order Multi-point Boundary Value Problems Research Articles

On some higher order boundary value problems at resonance with integral boundary conditions

This paper investigates the existence of solutions for higher-order multipoint boundary value problems at resonance. We obtain existence results by using coincidence degree arguments.

A Barycentric Interpolation Collocation Method for Linear Nonlocal Boundary Value Problems

This paper is devoted to the numerical treatment of a class of higher-order multi-point boundary value problem-s(BVPs). The method is proposed based on the Lagrange interpolation collocation method, but it avoids thenumerical instability of Lagrange interpolation. Numerical results obtained by present method compare with othermethods show that the present method is simple and accurate for higher-order multi-point BVPs, and it is eectivefor solving six order or higher order multi-point BVPs.

ERRATUM ON THE ARTICLE ‘POSITIVE SOLUTIONS FOR SINGULAR SYSTEMS OF HIGHER-ORDER MULTI-POINT BOUNDARY VALUE PROBLEMS’ (DOI: 10.3846/13926292.2013.804009)

"Erratum on the article ‘Positive solutions for singular systems of higher-order multi-point boundary value problems ’ (doi: 10.3846/13926292.2013.804009)." Mathematical Modelling and Analysis, 18(3), p. 461

Existence of positive solutions for a system of higher-order multi-point boundary value problems

We investigate the existence of positive solutions of a system of higher-order nonlinear ordinary differential equations, subject to multi-point boundary conditions.

Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems

We investigate the existence and multiplicity of positive solutions of multi-point boundary value problems for systems of nonlinear higher-order ordinary differential equations.

On a system of higher-order multi-point boundary value problems

On a system of higher-order multi-point boundary value problems

Positive solutions for a system of higher-order multi-point boundary value problems

We present some results for positive solutions of a system of higher-order nonlinear ordinary differential equations, subject to multi-point boundary conditions.

A fourth-order compact finite difference method for nonlinear higher-order multi-point boundary value problems

A fourth-order compact finite difference method is proposed for a class of nonlinear 2 n th-order multi-point boundary value problems. The multi-point boundary condition under consideration includes various commonly discussed boundary conditions, such as the three- or four-point boundary condition, ( n + 2 ) -point boundary condition and 2 ( n − m ) -point boundary condition. The existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear term. The convergence and the fourth-order accuracy of the method are proved. An efficient monotone iterative algorithm is developed for solving the resulting nonlinear finite difference systems. Various sufficient conditions for the construction of upper and lower solutions are obtained. Some applications and numerical results are given to demonstrate the high efficiency and advantages of this new approach.

Solvability for Two Classes of Higher-Order Multi-Point Boundary Value Problems at Resonance

Using the theory of coincidence degree, we establish existence results of positive solutions for higher-order multi-point boundary value problems at resonance for ordinary differential equation , with one of the following boundary conditions: , and , , where is a continuous function, , all the have not the same sign. We also give some examples to demonstrate our results.