Entire solutions of certain type of non-linear differential equations

Year, pages: 2020, 87 - 94

Utilizing Nevanlinna's value distribution theory of meromorphic functions, we study transcendental entire solutions of the following type nonlinear differential equations in the complex plane \[ fⁿ(z)+P(z,f,f',…,f^(t))=P₁\e^α₁z+P₂\e^α₂z+P₃\e^α₃z, \] where $P_j$ and $α_i$ are nonzero constants for $j = 1,2,3$, such that $|α₁| > |α₂| > |α₃|$ and $P(z,f,f',…,f^(t) )$ is an algebraic differential polynomial in $f(z)$ of degree no greater than $n-1$.

Xue, B. 2020. Entire solutions of certain type of non-linear differential equations. In Mathematica Slovaca, vol. 70, no.1, pp. 87-94. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0334

Xue, B. (2020). Entire solutions of certain type of non-linear differential equations. Mathematica Slovaca, 70(1), 87-94. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0334

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava