The Periodicity of Entire Functions with Finite Order

Periodicity in a System of Differential Equations with Finite Delay

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

PERIODICITY OF HIGH - ORDER NEURAL FUNCTIONS Research

On the Number of Zeros of Successive Derivatives of Entire Functions of Finite Order

1 We use this occasion to point out that the condition lim inf log M (r) < 1 r-+c g(r) in Theorem 2 of [1] can be replaced by the somewhat weaker condition : there exists a, sequence r1, + oo such that log M (r,,) < g(r1,). It is clear from the proof that only this is actually used . Thus the following assertion is true THEOREM B. Let g(r) denote an arbitrary increasing function, defined in 0 <...

Coupled systems of equations with entire and polynomial functions

We consider the coupled system$F(x,y)=G(x,y)=0$,where$$F(x, y)=bs 0 {m_1}   A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$.We    derive a priory estimates  for the sums of the rootsof the considered system andfor the counting function of  roots.

On some results of entire functions of two complex variables using their relative lower order

Some basic properties relating to relative lower order of entire functions of two complex variables are discussed in this paper.