A Representative Solution to m-Order Linear Ordinary Differential Equation with Non local Conditions by Green%26apos;s Functional Concept

作者：Ozen Kemal^*; Orucoglu Kamil

来源：Mathematical Modelling and Analysis, 2012, 17(4): 571-588.

DOI：10.3846/13926292.2012.709471

• Green%26apos
• s function
• nonlocal boundary condition
• nonlocal integral condition
• boundary value problem
• adjoint problem

In this work, we investigate a linear completely nonhomogeneous nonlocal multipoint problem for an m-order ordinary differential equation with generally variable nonsmooth coefficients satisfying some general properties such as p-integrability and boundedness. A system of m + 1 integro-algebraic equations called the special adjoint system is constructed for this problem. Green%26apos;s functional is a solution of this special adjoint system. Its first component corresponds to Green%26apos;s function for the problem. The other components correspond to the unit effects of the conditions. A solution to the problem is an integral representation which is based on using this new Green%26apos;s functional. Some illustrative implementations and comparisons are provided with some known results in order to demonstrate the advantages of the proposed approach.

• 出版日期2012