FORMS OF ENTIRE SOLUTIONS OF PARTIAL DIFFERENTIAL DIFFERENCE EQUATIONS WITH CONSTANT COEFFICIENTS

. 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.