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On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate

Lucas Jódar, Enrique A. Navarro (1989)

Aplikace matematiky

In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...

On the global dynamics of the cancer AIDS-related mathematical model

Konstantin E. Starkov, Corina Plata-Ante (2014)

Kybernetika

In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive...

On the growth of an algebroid function with radially distributed values

Nan Wu, Jian Hua Zheng (2015)

Annales Polonici Mathematici

We investigate how the growth of an algebroid function could be affected by the distribution of the arguments of its a-points in the complex plane. We give estimates of the growth order of an algebroid function with radially distributed values, which are counterparts of results for meromorphic functions with radially distributed values.

On the growth of solutions of some higher order linear differential equations

Abdallah El Farissi, Benharrat Belaidi (2012)

Applications of Mathematics

In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation f ( k ) + A k - 1 f ( k - 1 ) + + A 2 f ' ' + ( D 1 ( z ) + A 1 ( z ) e a z ) f ' + ( D 0 ( z ) + A 0 ( z ) e b z ) f = F ( k 2 ) , where a , b are complex constants that satisfy a b ( a - b ) 0 and A j ( z ) ( j = 0 , 1 ...

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