Poincaré theorem and nonlinear PDE's

• Autorzy: Maria E. Pliś
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Laplace distributions; Laplace transforms; formal solutions

Kategorie tematyczne

• 46F20: Distributions and ultradistributions as boundary values of analytic functions
• 44A10: Laplace transform

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 69
• Numer: 2
• Strony: 99-105

Daty

wydano

1998

otrzymano

1996-12-16

poprawiono

1997-11-05

Twórcy

autor

Maria E. Pliś

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

Bibliografia

• [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).