Poincaré theorem and nonlinear PDE's

Maria E. Pliś

Annales Polonici Mathematici (1998)

  • Volume: 69, Issue: 2, page 99-105
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Maria E. Pliś. "Poincaré theorem and nonlinear PDE's." Annales Polonici Mathematici 69.2 (1998): 99-105. <http://eudml.org/doc/270474>.

@article{MariaE1998,
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.},
author = {Maria E. Pliś},
journal = {Annales Polonici Mathematici},
keywords = {Laplace distributions; Laplace transforms; formal solutions},
language = {eng},
number = {2},
pages = {99-105},
title = {Poincaré theorem and nonlinear PDE's},
url = {http://eudml.org/doc/270474},
volume = {69},
year = {1998},
}

TY - JOUR
AU - Maria E. Pliś
TI - Poincaré theorem and nonlinear PDE's
JO - Annales Polonici Mathematici
PY - 1998
VL - 69
IS - 2
SP - 99
EP - 105
AB - 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.
LA - eng
KW - Laplace distributions; Laplace transforms; formal solutions
UR - http://eudml.org/doc/270474
ER -

References

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  1. [1] V. I. Arnold, Additional Topics in the Theory of Ordinary Differential Equations, Nauka, Moscow, 1978 (in Russian). 
  2. [2] A. Bobylev, Poincaré theorem, Boltzmann equation and KdV-type equations, Dokl. Akad. Nauk SSSR 256 (1981), 1341-1346 (in Russian). 
  3. [3] R. R. Rosales, Exact solutions of some nonlinear evolution equations, Stud. Appl. Math. 59 (1978), 117-151. Zbl0387.35061
  4. [4] Z. Szmydt and B. Ziemian, Laplace distributions and hyperfunctions on ℝ̅ⁿ₊, J. Math. Sci. Tokyo 5 (1998), 41-74. 
  5. [5] B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996). 

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