A Gap Theorem for Power Series Solutions of Algebraic Differential Equations

Leonard Lipshitz; Lee A. Rubel

doi:10.2307/2374602

A Gap Theorem for Power Series Solutions of Algebraic Differential Equations

American Journal of Mathematics ◽

10.2307/2374602 ◽

1986 ◽

Vol 108 (5) ◽

pp. 1193 ◽

Cited By ~ 13

Author(s):

Leonard Lipshitz ◽

Lee A. Rubel

Keyword(s):

Power Series ◽

Differential Equations ◽

Series Solutions ◽

Algebraic Differential Equations ◽

Gap Theorem ◽

Power Series Solutions

Download Full-text

Power series solutions of algebraic differential equations

Mathematische Annalen ◽

10.1007/bf01579200 ◽

1984 ◽

Vol 267 (2) ◽

pp. 213-238 ◽

Cited By ~ 32

Author(s):

J. Denef ◽

L. Lipshitz

Keyword(s):

Power Series ◽

Differential Equations ◽

Series Solutions ◽

Algebraic Differential Equations ◽

Power Series Solutions

Download Full-text

Arithmetic Properties of Power Series Solutions of Algebraic Differential Equations

Annals of Mathematics ◽

10.2307/1971135 ◽

1981 ◽

Vol 113 (1) ◽

pp. 111 ◽

Cited By ~ 5

Author(s):

Yasutaka Sibuya ◽

Steven Sperber

Keyword(s):

Power Series ◽

Differential Equations ◽

Series Solutions ◽

Algebraic Differential Equations ◽

Arithmetic Properties ◽

Power Series Solutions

Download Full-text

Some New Results on Power-Series Solutions of Algebraic Differential Equations

Singular Perturbations and Asymptotics ◽

10.1016/b978-0-12-493260-9.50019-9 ◽

1980 ◽

pp. 379-404

Author(s):

Yasutaka Sibuya ◽

Steven Sperber

Keyword(s):

Power Series ◽

Differential Equations ◽

Series Solutions ◽

Algebraic Differential Equations ◽

Power Series Solutions

Download Full-text

Power Series Solutions of Ordinary Differential Equations

Differential Equations with Mathematica ◽

10.1016/b978-0-12-041539-7.50009-3 ◽

1993 ◽

pp. 216-271

Author(s):

Martha L. Abell ◽

James P. Braselton

Keyword(s):

Power Series ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Series Solutions ◽

Power Series Solutions

Download Full-text

Power Series Solutions of Differential Equations

A Short Course in Mathematical Methods with Maple ◽

10.1142/9789812775078_0011 ◽

2005 ◽

pp. 539-566

Keyword(s):

Power Series ◽

Differential Equations ◽

Series Solutions ◽

Power Series Solutions

Download Full-text

Random Hermite differential equations: Mean square power series solutions and statistical properties

Applied Mathematics and Computation ◽

10.1016/j.amc.2011.09.008 ◽

2011 ◽

Vol 218 (7) ◽

pp. 3654-3666 ◽

Cited By ~ 9

Author(s):

G. Calbo ◽

J.-C. Cortés ◽

L. Jódar

Keyword(s):

Power Series ◽

Differential Equations ◽

Statistical Properties ◽

Mean Square ◽

Series Solutions ◽

Power Series Solutions

Download Full-text

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 ◽

Cited By ~ 32

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 ◽

Formal Power

Download Full-text

Generalised power series solutions of sub-analytic differential equations

Comptes Rendus Mathematique ◽

10.1016/j.crma.2005.11.005 ◽

2006 ◽

Vol 342 (2) ◽

pp. 99-102

Author(s):

Mickaël Matusinski ◽

Jean-Philippe Rolin

Keyword(s):

Power Series ◽

Differential Equations ◽

Series Solutions ◽

Power Series Solutions

Download Full-text

Formal and convergent power series solutions of singular partial differential equations

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-1979-0546913-5 ◽

1979 ◽

Vol 256 ◽

pp. 163-163 ◽

Cited By ~ 5

Author(s):

Stanley Kaplan

Keyword(s):

Partial Differential Equations ◽

Power Series ◽

Differential Equations ◽

Series Solutions ◽

Convergent Power Series ◽

Partial Differential ◽

Power Series Solutions

Download Full-text

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 ◽

Cited By ~ 17

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 ◽

Formal Power

Download Full-text