A note on properties of solutions of Riccati and hyper‐Riccati equations

Abstract

The paper focuses on transcendental meromorphic solutions of Riccati and hyper-Riccati equations and their value distribution properties. Special attention is paid to deficient values in various senses, in particular to deficient values in the sense of Petrenko in the case of solutions of finite order. The question of small deficient functions is also considered. The estimates of deficiencies, multiplicity indices and, in the case of functions of finite order, also deviations from small functions are presented. K E Y W O R D S meromorphic function, Riccati equation, value distribution M S C ( 2 0 1 0 ) 30D35, 34M05

Special issue devoted to the 14th International conference “Dynamical Systems — Theory and Applications”

“…Next, by defining dynamical systems, stability and bifurcation are investigated for states of thermo‐mechanic solids. Conditions for stability and generic bifurcation are presented for constitutive relations under consideration. A note on properties of solutions of Riccati and hyper‐Riccati equations , by Ciechanowicz is concentred on general aspects of transcendental meromorphic solutions of Riccati and hyper‐Riccati equations as well as their properties of value distribution. Special attention is focused to deficient values in different senses, in particular to deficient values in the sense of Petrenko in the case of solutions of finite order.…”

“…A note on properties of solutions of Riccati and hyper‐Riccati equations , by Ciechanowicz is concentred on general aspects of transcendental meromorphic solutions of Riccati and hyper‐Riccati equations as well as their properties of value distribution. Special attention is focused to deficient values in different senses, in particular to deficient values in the sense of Petrenko in the case of solutions of finite order.…”