Meromorphic solutions for the Fermat-type differential-difference equations (Q6637610)

By using Nevanlinna theory and its difference analogues, the authors study the entire solutions with hyper-order less than one to the following differential-difference equation \N\[\Nf(z)^{n}+(f'(z+c))^{m}=p(z)e^{r(z)}+q(z)e^{s(z)}.\N\]\NThey classify the above equation into three cases: \N\[\Nf(z)^{n}+(f'(z+c))^{m}=P_{1}(z)e^{A_{1}z^{k}}+Q_{1}(z)e^{B_{1}z^{k}},\N\]\N\[\Nf(z)^{n}+(f'(z+c))^{m}=P_{2}(z)e^{A_{2}z^{k}},\N\]\Nand \N\[\Nf(z)^{n}+(f'(z+c))^{m}=P_{3}(z)e^{A_{3}z^{k}}+Q_{3}(z),\N\]\Nand obtain three main results which improve the earlier related results.