Skip to main content
Log in

Meromorphic solutions of generalized Schröder equations

  • Published:
Aequationes mathematicae Aims and scope Submit manuscript


We consider meromorphic solutions of functional equations of the form¶¶\( f(cz) = R(z,f(z)) = {\sum_{j=0}^pa_j(z)f(z)^j \over \sum_{j=0}^q b_j(z)f(z)^j} \),¶where the coefficients a j (z),b j (z) are meromorphic functions and c is a complex constant. In fact, for \( |c| > 1 \), any local meromorphic solution around the origin has a meromorphic continuation over \( {\Bbb C} \). We prove a number of results on the growth and value distribution of solutions. In the special case of¶¶\( f(cz) = A(z) + \gamma f(z) + \delta f(z)^2 \),¶where \( c, \gamma, \delta \in {\Bbb C} \), \( |c|>1 \), \( \delta \neq 0 \), and A(z) is entire, we offer a detailed analysis on the number of distinct meromorphic solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Author information

Authors and Affiliations


Additional information

Received: March 16, 2000, revised version: August 26, 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gundersen, G., Heittokangas, J., Laine, I. et al. Meromorphic solutions of generalized Schröder equations. Aequat. Math. 63, 110–135 (2002).

Download citation

  • Published:

  • Issue Date:

  • DOI: