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Discussion on the analytic solutions of the second-order iterated differential equation

Han Ze Liu|Wen Rong Li
대한수학회 (The Korean Mathematical Society)|2006.11|대한수학회보 (Bulletin of the KMS)|제43권 제4호|pp. 791-804

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초록

Abstract

This paper is concerned with a second-order iterateddierential equation of the formc0x00(z)+ c1x0(z)+ c2x(z) = x(az+bx(z)) + h(z) with the distinctive feature that the argument of theunknown function depends on the state. By constructing a conver-gent power series solution of an auxiliary equation, analytic solu-tions of the original equation are obtained.

참고문헌 (8)

  1. "Functional series" (1970), Gordon & Breach
  2. "Analytic solutions for a class second-order iterative functional-dier-ential equation", 41(1), pp.167~176 (1998)
  3. "Analytic solutions of an iterative functional equation", 68(1-2), pp.21~27 (2004)
  4. "On a boundary value problem", 3, pp.252~255 (1965)
  5. "Analytic solutions of an iterative functionaldierential equation", 33(6), pp.47~51 (1997)
  6. "Analytic solutions of a functional-dierential equationwith state dependent argument", 1(4), pp.471~480 (1997)
  7. "Analytic solutions of a second-order functional di？？erentialequation with a state dependent delay", 39(3-4), pp.345~352 (2001)
  8. "Iteration of analytic functions Ann. of Math.", pp.612~ (1942)

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