Download PDF - Poincaré theorem and nonlinear PDE'sAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Poincaré theorem and nonlinear PDE's

Authors 1

Affiliations

  1. Institute of Mathematics, Cracow Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Abstract

A family of formal solutions of some type of nonlinear partial differential equations is found. Terms of such solutions are Laplace transforms of some Laplace distributions. The series of these distributions are locally finite.

Keywords

ENG
Laplace distributions, Laplace transforms, formal solutions

Bibliography

  1. V. I. Arnold, Additional Topics in the Theory of Ordinary Differential Equations, Nauka, Moscow, 1978 (in Russian).
  2. A. Bobylev, Poincaré theorem, Boltzmann equation and KdV-type equations, Dokl. Akad. Nauk SSSR 256 (1981), 1341-1346 (in Russian).
  3. R. R. Rosales, Exact solutions of some nonlinear evolution equations, Stud. Appl. Math. 59 (1978), 117-151.
  4. Z. Szmydt and B. Ziemian, Laplace distributions and hyperfunctions on ℝ̅ⁿ₊, J. Math. Sci. Tokyo 5 (1998), 41-74.
  5. B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996).
Annales Polonici Mathematici
1998/69/2
Export to PBN, Opens in new tab
Pages:
99-105
Main language of publication
English
Received
1996-12-16
Accepted
1997-11-05
Published
1998
Exact and natural sciences