On entire solutions of \(f^{2}(z)+cf'(z)=h(z)\) (Q657664)
From MaRDI portal
| This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On entire solutions of \(f^{2}(z)+cf'(z)=h(z)\) |
scientific article; zbMATH DE number 5996085
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On entire solutions of \(f^{2}(z)+cf'(z)=h(z)\) |
scientific article; zbMATH DE number 5996085 |
Statements
On entire solutions of \(f^{2}(z)+cf'(z)=h(z)\) (English)
0 references
10 January 2012
0 references
The existence of meromorphic solutions of differential equations in the complex plane is an interesting topic. In this paper, the authors consider nonlinear differential equations of the form \[ f^{2}(z)+cf'(z)=h(z), \] where \(h(z)\) is entire function and whose zeros form an \(A\)-set. It is proved that the above equation has no entire solution. Moreover, the authors give an example to show that the conjecture in [\textit{C.-C. Yang}, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 49, 27--29 (1970; Zbl 0218.30030)] is not true.
0 references
value distribution theory
0 references
differential equations
0 references
entire solution
0 references
generalized \(A\)-set
0 references