The Existence and Uniqueness of Solutions to Systems of Second-order Ordinary Differential Equations Boundary Value Problem in Absract Space

Chinese Quarterly Journal of Mathematics ›› 2011, Vol. 26 ›› Issue (4): 573-577.

The Existence and Uniqueness of Solutions to Systems of Second-order Ordinary Differential Equations Boundary Value Problem in Absract Space

1. School of Science, University of Science and Technology Liaoning2. School of Science, Northeastern University

Received:2009-09-02 Online:2011-12-30 Published:2023-04-14
About author:WU Li-bing(1980-), male, native of Chaoyang, a lecturer of University of Science and Technology Liaoning, M.S.D., engages in nonlinear function analysis and application; SUN Tao(1959-), male, native of Shenyang, Liaoning, an associate professor of Northeastern University, engages in nonlinear function analysis; HE Xi-qin(1964-), male, native of Huaining, Anhui, a professor of University of Science and Technology Liaoning, Ph.D., engages in modern control theory and nonlinear function analysis.

Abstract

Abstract: In this paper, it is discussed by using cone and upper and lower solutions mono- tone iterative theory of mixed monotone operator that the bounary value problem is more generalized style to system of equations in the form of -u... v(0) = v(1) = 0 in abstract space. Moreover, it is obtained unique solutions for system of equations and error estimations between approximation iteration sequence and exact solution under more simpler conditions. Therefore, some new results which extend and improve the related known works in the literatures are obtained.

Key words: systems of equations, bounary value problem, cone, approximation solution

CLC Number:

O175.8

WU Li-bing, SUN Tao, HE Xi-qin. The Existence and Uniqueness of Solutions to Systems of Second-order Ordinary Differential Equations Boundary Value Problem in Absract Space[J]. Chinese Quarterly Journal of Mathematics, 2011, 26(4): 573-577.

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The Existence and Uniqueness of Solutions to Systems of Second-order Ordinary Differential Equations Boundary Value Problem in Absract Space

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