On entire solutions of $f^{2}(z)+cf'(z)=h(z)$

Abstract

We investigate the existence of entire solutions of non-linear differential equations of type $f^{2}(z)+cf'(z)=h(z),$ where $h(z)$ is a given entire function, whose zeros form an $A-$set. As a by-product of the studies, we give a negative answer to an open question raised in [4].