Meromorphic Solutions for a Class of Differential Equations and Their Applications
| Autor: | Weiran Lü, Jing Yang, Linlin Wu, Feng Lü |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Class (set theory) Control and Optimization Degree (graph theory) Differential equation Applied Mathematics Entire function 010102 general mathematics Function (mathematics) 01 natural sciences 010101 applied mathematics 0101 mathematics Analysis Mathematics Algebraic differential equation Differential polynomial Meromorphic function |
| Zdroj: | Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences). 53:260-265 |
| ISSN: | 1934-9416 1068-3623 |
| DOI: | 10.3103/s1068362318050023 |
| Popis: | In this note, we study the admissible meromorphic solutions for algebraic differential equation fnf' + Pn−1(f) = R(z)eα(z), where Pn−1(f) is a differential polynomial in f of degree ≤ n − 1 with small function coefficients, R is a non-vanishing small function of f, and α is an entire function. We show that this equation does not possess any meromorphic solution f(z) satisfying N(r, f) = S(r, f) unless Pn−1(f) ≡ 0. Using this result, we generalize a well-known result by Hayman. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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