scholarly journals Polynomial Solutions and Annihilators of Ordinary Integro-Differential Operators* *G.R. was supported by the Austrian Science Fund (FWF): J 3030-N18.

2013 ◽  
Vol 46 (2) ◽  
pp. 308-313 ◽  
Author(s):  
Alban Quadrat ◽  
Georg Regensburger
Keyword(s):  
Differential Operators ◽  
Polynomial Solutions ◽  
Austrian Science Fund

A Study on Rational Solutions to a KP-like Equation

2015 ◽  
Vol 70 (4) ◽  
pp. 263-268 ◽  
Author(s):  
Yufeng Zhang ◽  
Wen-Xiu Ma
Keyword(s):  
Differential Equation ◽  
Prime Number ◽  
Nonlinear Differential Equation ◽  
Symbolic Computation ◽  
Bilinear Form ◽  
Differential Operators ◽  
Rational Solutions ◽  
Polynomial Solutions ◽  
Bilinear Equation

AbstractA KP-like nonlinear differential equation is introduced through a generalised bilinear equation which possesses the same bilinear form as the standard KP bilinear equation. By symbolic computation, nine classes of rational solutions to the resulting KP-like equation are generated from a search for polynomial solutions to the corresponding generalised bilinear equation. Three generalised bilinear differential operators adopted are associated with the prime number p=3.

On Linear Ordinary Differential Equation With Orthogonal Polynomial Solutions

2018 ◽  
Vol 1 (20) ◽  
pp. 559-572
Author(s):  
ولدان وليد محمود
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Fourth Order ◽  
Differential Operators ◽  
Linear Ordinary Differential Equation ◽  
Large Piece ◽  
Polynomial Solutions ◽  
The Subject

: The subject of orthogonal polynomials cuts across a large piece of mathematics and its applications. In this paper we give a  survey of the orthogonal polynomial solutions of second-order and fourth-order linear ordinary differential equation, on the generated self-adjoint differential operators .

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

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