Dong Ming-de. New Theory for Equations of Non-Fuchsian Type Representation Theorem of Tree Series Solution(I)[J]. Applied Mathematics and Mechanics, 1984, 5(5): 647-663.
Citation: Dong Ming-de. New Theory for Equations of Non-Fuchsian Type Representation Theorem of Tree Series Solution(I)[J]. Applied Mathematics and Mechanics, 1984, 5(5): 647-663.

New Theory for Equations of Non-Fuchsian Type Representation Theorem of Tree Series Solution(I)

  • Received Date: 1983-09-09
  • Publish Date: 1984-10-15
  • In the analytic theory of differential equations the exact explicit analytic solution has not been obtained for equations of the non-Fuchsian type(Poincare's problem). The new theory proposed in this paper for the first time affords a general method of finding exact analytic expres-sion for irregular integrals.By discarding the assumption of formal solution of classical theory,our method consists in deriving a cor-respondence relation from the equation itself and providing the analytic structure of irregular integrals naturally by the residue theorem. Irregular integrals are made up of three parts: noncontracted part,represented by ordinary recursion series,all-and semi-contracted part by the so-called tree series. Tree series solutions belong to analytic function of the new kind with recursion series as the special case only.
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  • [1]
    Poincare,H.,Acta Math.,T.I.(1887) 310-332,Oeuvres T.I.(1882) 333-335.
    [2]
    Hill,G.W.,Am.J.Math.,T.I.(1878) Acta Math.TVⅢ(1886).
    [3]
    Dong Ming-de,Acta Astronomic Sinica,V.12,1(1980).
    [4]
    Dong Ming-de,Poincare's Problem of Irregular Integrals,Lecture Notes(unpublished).
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