Convolution equations in the space of Laplace distributions

Maria Pliś

ArticleOriginal scientific text

Title

Convolution equations in the space of Laplace distributions

Authors ¹

Affiliations

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

Abstract

A formal solution of a nonlinear equation P(D)u = g(u) in 2 variables is constructed using the Laplace transformation and a convolution equation. We assume some conditions on the characteristic set Char P.

Keywords

ENG

Laplace distributions, Laplace transforms, convolution equations

[B] L. Bieberbach, $Δ u = e^{u}$ und die automorphen Funktionen, Math. Ann. 77 (1916), 173-212.
[P] M. E. Pliś, Poincaré theorem and nonlinear PDE's, Ann. Polon. Math. 69 (1998), 99-105.
[P-Z] M. E. Pliś and B. Ziemian, Borel resummation of formal solutions to nonlinear Laplace equations in $2$ variables, Ann. Polon. Math. 67 (1997), 31-41.
[Po] A. G. Popov, The non-euclidean geometry and differential equations, in: Banach Center Publ. 33, Inst. Math., Polish Acad. Sci., 1996, 297-308.
[S-Z] Z. Szmydt and B. Ziemian, Laplace distributions and hyperfunctions on ℝ̅ⁿ₊, J. Math. Sci. Univ. Tokyo 5 (1998), 41-74.

Title

Convolution equations in the space of Laplace distributions

Affiliations

Abstract

Keywords

Bibliography