Existence and uniqueness theorems for formal power series solutions of analytic differential systems

Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99 ◽

10.1145/309831.309875 ◽

1999 ◽

Author(s):

C. J. Rust ◽

G. J. Reid ◽

A. D. Wittkopf

Keyword(s):

Power Series ◽

Formal Power Series ◽

Existence And Uniqueness ◽

Uniqueness Theorems ◽

Series Solutions ◽

Differential Systems ◽

Existence And Uniqueness Theorems ◽

Power Series Solutions ◽

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Multisummability of formal power series solutions of partial differential equations with constant coefficients

Journal of Differential Equations ◽

10.1016/j.jde.2004.02.002 ◽

2004 ◽

Vol 201 (1) ◽

pp. 63-74 ◽

Author(s):

Werner Balser

Keyword(s):

Partial Differential Equations ◽

Power Series ◽

Differential Equations ◽

Formal Power Series ◽

Series Solutions ◽

Partial Differential ◽

Power Series Solutions ◽

Constant Coefficients ◽

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Formal power series solutions in a parameter

Journal of Differential Equations ◽

10.1016/s0022-0396(02)00083-9 ◽

2003 ◽

Vol 190 (2) ◽

pp. 559-578 ◽

Author(s):

Yasutaka Sibuya

Keyword(s):

Power Series ◽

Formal Power Series ◽

Series Solutions ◽

Power Series Solutions ◽

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Gevrey Order of Formal Power Series Solutions of Inhomogeneous Partial Differential Equations with Constant Coefficients

Funkcialaj Ekvacioj ◽

10.1619/fesi.53.411 ◽

2010 ◽

Vol 53 (3) ◽

pp. 411-434 ◽

Author(s):

Werner Balser ◽

Masafumi Yoshino

Keyword(s):

Partial Differential Equations ◽

Power Series ◽

Differential Equations ◽

Formal Power Series ◽

Series Solutions ◽

Partial Differential ◽

Power Series Solutions ◽

Constant Coefficients ◽

Gevrey Order ◽

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Formal power series solutions of the heat equation in one spatial variable

Differential Equations and Quantum Groups ◽

10.4171/020-1/4 ◽

2009 ◽

pp. 49-58 ◽

Author(s):

Werner Balser

Keyword(s):

Power Series ◽

Heat Equation ◽

Formal Power Series ◽

Spatial Variable ◽

Series Solutions ◽

Power Series Solutions ◽

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Summability of Formal Power-Series Solutions of Partial Differential Equations with Constant Coefficients

Journal of Mathematical Sciences ◽

10.1023/b:joth.0000047246.49736.b0 ◽

2004 ◽

Vol 124 (4) ◽

pp. 5085-5097 ◽

Author(s):

Werner Balser

Keyword(s):

Partial Differential Equations ◽

Power Series ◽

Differential Equations ◽

Formal Power Series ◽

Series Solutions ◽

Partial Differential ◽

Power Series Solutions ◽

Constant Coefficients ◽

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Multisummability of formal power series solutions of linear ordinary differential equations

Asymptotic Analysis ◽

10.3233/asy-1991-5102 ◽

1991 ◽

Vol 5 (1) ◽

pp. 27-45 ◽

Author(s):

W. Balser ◽

B.L.J. Braaksma ◽

J.-P. Ramis ◽

Y. Sibuya

Keyword(s):

Power Series ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Formal Power Series ◽

Series Solutions ◽

Linear Ordinary Differential Equations ◽

Power Series Solutions ◽

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An algorithm of multisummation of formal power series, solutions of linear ODE equations

Mathematics and Computers in Simulation ◽

10.1016/s0378-4754(96)00016-x ◽

1996 ◽

Vol 42 (4-6) ◽

pp. 409-425 ◽

Author(s):

F. Jung ◽

F. Naegele ◽

J. Thomann

Keyword(s):

Power Series ◽

Formal Power Series ◽

Series Solutions ◽

Power Series Solutions ◽

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Multisummability of formal power series solutions of nonlinear meromorphic differential equations

Annales de l’institut Fourier ◽

10.5802/aif.1301 ◽

1992 ◽

Vol 42 (3) ◽

pp. 517-540 ◽

Author(s):

Boele L. J. Braaksma

Keyword(s):

Power Series ◽

Differential Equations ◽

Formal Power Series ◽

Series Solutions ◽

Power Series Solutions ◽

Formal Power ◽

Meromorphic Differential

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Convergence of formal power series solutions of a system of nonlinear differential equations at an irregular singular point

Lecture Notes in Mathematics - Geometrical Approaches to Differential Equations ◽

10.1007/bfb0089978 ◽

1980 ◽

pp. 135-142 ◽

Author(s):

Yasutaka Sibuya

Keyword(s):

Singular Point ◽

Power Series ◽

Differential Equations ◽

Formal Power Series ◽

Nonlinear Differential Equations ◽

Series Solutions ◽

Irregular Singular Point ◽

Power Series Solutions ◽

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Small divisor problems and divergent formal power series solutions

Journal of the Mathematical Society of Japan ◽

10.2969/jmsj/05040903 ◽

1998 ◽

Vol 50 (4) ◽

pp. 903-913

Author(s):

Masafumi YOSHINO

Keyword(s):

Power Series ◽

Formal Power Series ◽

Series Solutions ◽

Small Divisor ◽

Power Series Solutions ◽

Divisor Problems ◽

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