Riccati differential equations with elliptic coefficients. II
Copyright policy )Riccati differential equations with elliptic coefficients. II
In this paper, the authors consider the Riccati differential equation \[ w'+w^2+a\wp(z)=0, \] where \(\wp(z)\) is the Weierstrass \(\wp\)-function satisfying \[ (\wp')^2 = 4\wp^3 - b, b \neq 0 \] and \[ a = (1 - m^2)/4, m \geq 2, m \neq 6n. \] They show under these conditions that all solutions to the Riccati differential equation are meromorphic and provide a full investigation of their periodicity and double periodicity.
- Kanazawa University Japan
- Nippon Institute of Technology Japan
- Keio University Japan
- University of Eastern Finland Finland
Riccati equation, Mermorphic function, Riccati differential equation, Oscillation, growth of solutions to ordinary differential equations in the complex domain, Nonlinear ordinary differential equations and systems, Entire and meromorphic solutions to ordinary differential equations in the complex domain, Weierstrass pe-function, Periodic solutions to ordinary differential equations, 34M05
Riccati equation, Mermorphic function, Riccati differential equation, Oscillation, growth of solutions to ordinary differential equations in the complex domain, Nonlinear ordinary differential equations and systems, Entire and meromorphic solutions to ordinary differential equations in the complex domain, Weierstrass pe-function, Periodic solutions to ordinary differential equations, 34M05
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