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C m solutions of systems of finite difference equations

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  • Xinhe Liu
  • Xiuli Zhao
  • Jianmin Ma

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 ) .

Suggested Citation

  • Xinhe Liu & Xiuli Zhao & Jianmin Ma, 2003. "C m solutions of systems of finite difference equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:964316
    DOI: 10.1155/S0161171203202131
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