Forms of entire solutions of partial differential difference equations with constant coefficients

Abstract

The purpose of this article is to describe the transcendental entire solutions of  quadratic trinomial partial differential equations (PDDEs) with constant coefficients.  We establish  theorems on the forms of finite order transcendental entire  solutions for such PDDEs, which generalize and improve previous theorems.  Some examples confirm the existence and the forms of transcendental entire  solutions with finite order of such equations.  For more information see https://ejde.math.txstate.edu/Volumes/2024/37/abstr.html