Clairaut Convolution Differential Equation

Abstract

The Clairaut convolution differential equation, a variant of the more general Clairaut equation, has been a subject of considerable interest in the realm of mathematical analysis. Based on an infinite dimensional test space of holomorphic functions, the purposes of this work are to investigate the convolution calculus in white noise theory to introduce and study the solution of the analogue of the Clairaut equation, called Clairaut convolution differential equation (CCDE). We study the Clairaut convolution differential equation as a natural counterpart of the classical Clairaut differential equation and give its general and singular solutions.

Keywords: Clairaut equation; Convolution derivative; Convolution differential equation.

2010 Mathematics Subject Classification. 54C40; 14E20; 46E25; 20C20