OSCILLATION CRITERIA OF NEUTRAL TYPE IMPULSIVE HYPERBOLIC EQUATIONS

In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new sufficient conditions for oscillation are presented.

EQUIVALENCES BETWEEN BLOCH TYPE SPACES AND BMO SPACES ON THE HYPERBOLIC DOmAINS IN C

For an analytic function f on the hyperbolic domain Ω in C,the following conclusions are obtained: (i)f∈B(Ω)=BMOA(Ω,m)if and only if Ref∈B(?)(Ω)=BMOH(Ω,m).(ii)QB_h(Ω)=B_h(Ω) (BMOH,(Ω,m)=BMOH(Ω,m)if and only if C(Ω)=inf{Z_o(z)·δ_o(z)·z≡Ω}>0,Also some applica- lions to automorphic function are considered.

Classification of Crystallographic Groups in the Hyperbolic 5-Dimensional Indefinite Space

Let V be a hyperbolic 5-dimensional indefinite space. W is the infinite Weyl group of an irreducible root system. The principal aim of this paper is to classify all crystallgraphic groups associated with W up to conjugation in the affine group A(V).

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF NEUTRAL HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH DELAYS

This paper is concerned with the oscillations of neutral hyperbolic partial differential equations with delays. Necessary and sufficient, conditions are obtained for the oscillations of all solutions of the equations, and these results are illustrated by some examples.