On entire solutions of certain partial differential equations

We firstly describe entire solutions of variation of the well-known PDE of tubular surfaces. In addition, we consider entire solutions of certain partial differential equations, which are related with the Picard’s little theorem. Moreover, we obtain a Tumura-Clunie type theorem in \({\mathbb {C}}^{m}\) ${\mathbb{C}}^m$ , which is an improvement of a result given by Hu-Yang (Bull Aust Math Soc 90: 444-456, 2014).