09-192 S. MALEK, C. STENGER

On complex singularity analysis of holomorphic solutions of linear partial differential equations (499K, Postscript) Oct 20, 09

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Abstract. We construct formal series solutions of linear partial differential equations as linear combinations of powers of solutions of first order nonlinear differential equations, following the classical tanh method. We give sufficient conditions under which the constructed formal series define holomorphic functions on some punctured polydiscs of C^2. Moreover, we study the rate of growth of these solutions near their singular points.

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