On entire solutions of nonlinear difference-differential equations (Q2872986)

The paper under review concerns the nonlinear differential-difference equation of the form NEWLINE\[NEWLINE f^n + Q(z, f) = hNEWLINE\]NEWLINE where \(n\geq 2\) is an integer, \(Q(z, f)\) is a differential-difference polynomial in \(f\) with polynomial coefficients, and \(h\) is a meromorphic function of order \(\leq 1\).NEWLINENEWLINEThe authors show, under two assumptions on \(Q(z, f)\), that the equation has no transcendental entire solutions of finite order. Their proofs use results from the Nevanlinna theory such as the estimates on the logarithmic derivatives, Clunie's Lemma and so on.