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

Ciechanowicz, Ewa

doi:10.1002/zamm.201800162

Cited by 2 publications

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“…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.…”

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“…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.…”

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

Awrejcewicz

2019

Z Angew Math Mech

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in Łódź, Poland. The content of the presented articles includes modern states and contemporary perspectives of mathematical modeling, simulation, stability, control and new mathematical methods addressed to nonlinear dynamical systems, both in theoretical aspects and practical applications.The Scientific Committee of the conference included the following well-known researchers: H. Altenbach -PREFACE 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. Moreover, the problem of small deficient functions is also considered in this study. Eventually, the estimates of deficiencies, multiplicity indices and, in the case of functions of finite order, deviations from small functions, are also presented.(6) Circular membrane with a centrally-located opening -analytical model using parameterization of the non-empty torus, by Waszczuk-Młyńska and Radkowski [6] proposed a model of circular membrane with an opening in its central part (damagesimulating opening). A novel partial differential equation of the analyzed system is computed by means of the Fourier method of separation of variables as well as applying the Bessel substitution. The correctness of the presented analytical model and the obtained results in the form of the natural frequency were verified based on the experimental tests and the numerical modeling.(7) Solving partial differential equations in computational mechanics via nonlocal numerical approaches, by Martowicz et al. [7] is addressed to solving partial differential equations for a continuum solid body by using a nonlocal formulation. The authors introduce a nonlocal finite difference scheme to show its applicability to computational mechanics. Moreover, potential areas of practical applications for the presented method are indicated. Using the proposed method, selected thermal and mechanical properties of a gas foil bearing (GFB) component and a rod-like structural part of GFB made of super alloy Inconel 625 are investigated numerically.We hope that scientific problems considered in this special issue will be interesting for readers of the Journal of Applied Mathematics and Mechanics. In here, we are very grateful to Prof. Holm Altenbach for invitation to edit this special issue. We would like also to thank all the Referees for their times, critical remarks and efforts in helping us to carry out the review process.

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

Awrejcewicz

2019

Z Angew Math Mech

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Properties of meromorphic solutions of certain equations via Nevanlinna theory

Ciechanowicz

2024

Contemporary Mathematics

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Special functions are functions encountered in the process of solving various problems in physics. In a natural way one of the directions concerning analysis of properties of special function is to examine them as solutions of linear differential equations. This line of thought can be extended not only to nonlinear ordinary differential equations, but also to difference equations and delay-differential equations. Well known examples of nonlinear ordinary differential equations with solutions expressed in terms of special functions include Riccati equations (Airy functions) and Painlevé equations (Airy functions for P 2 P_2 , Bessel functions for P 3 P_3 or Whittaker functions for P 4 P_4 ). Painlevé transcendents have been thoroughly examined by means of global Nevanlinna theory, resulting in estimates of growth, descriptions of distribution of zeros and poles, analysis of existence of exceptional and ramified values. It has also provided insight into behaviour of special functions involved. Recent development of difference Nevanlinna theory opened similar possibilities of analysis of behaviour of solutions of difference and delay-differential equations in general, and various involved special functions in particular.

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

Cited by 2 publications

References 22 publications

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

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

Properties of meromorphic solutions of certain equations via Nevanlinna theory

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