C m solutions of systems of finite difference equations

Xinhe Liu, Xiuli Zhao and Jianmin Ma

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-12

Abstract:

Let ℝ be the real number axis. Suppose that G , H are C m maps from ℝ 2 n + 3 to ℝ . In this note, we discuss the system of finite difference equations G ( x , f ( x ) , f ( x + 1 ) , … , f ( x + n ) , g ( x ) , g ( x + 1 ) , … , g ( x + n ) ) + 0 and H ( x , g ( x ) , g ( x + 1 ) , … , g ( x + n ) , f ( x ) , f ( x + 1 ) , … , f ( x + n ) ) = 0 for all x ∈ ℝ , and give some relatively weak conditions for the above system of equations to have unique C m solutions ( m ≥ 0 ) .

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:964316

DOI: 10.1155/S0161171203202131

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