On a Delay Reaction-Diffusion Difference Equation of Neutral Type

Shi, Bao
October 2002
Acta Mathematica Sinica;2002, Vol. 18 Issue 4, p755
Academic Journal
In this paper, we first consider a delay diffrence equation of neutral type of the form: Δ(y[SUBn]+py[SUBn-k]) + q[SUBn]y[SUBn-l] = 0 for n ∈ Z[SUP+](0) (1∗) and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241-248) to guarantee that every non-oseillatory solution of (1∗) with p = 1 tends to zero as n → ∞. Moreover, we eonsider a delay reaction-diffusion difference equation of neutral type of the form: Δ[SUB1](u[SUBn,m] + pu[SUBn-k,m]) + q[SUBn,m] u[SUBn-l,m] = a[SUP2] Δ[SUP2,SUB2]] u[SUBn+1,m-1] for (n, m) &isin Z[SUP+] (0) × Ω, (2∗) study various cases of p in the neutral terra and obtain that if p ≥ -1 then every non-oscillatory solution of (2∗) tends uniformly in ∈ Ω to zero as n → ∞; if p = -1 then every solution of (2∗) oseillates and if p < -1 then every non-oscillatory solution of (2∗) goes uniformly in m ∈ Ω to infinity or minus infinity as n → ∞ under some hypotheses.


Related Articles

  • Initial conditions for optimal growth in a coupled ocean-atmosphere model of ENSO. Thompson, C.J. // Journal of the Atmospheric Sciences;2/15/98, Vol. 55 Issue 4, p537 

    Provides information on the development of a lineralized version of the Battisti model with a time-invariant background state. Information on the model equation; Detailed information on optimizing on SST versus optimizing on dynamics; Conclusion reached.

  • New oscillation criteria for a class of nonlinear delay... Tian, Chuan Jun; Zhang, B.G. // Nonlinear Studies;1998, Vol. 5 Issue 1, p35 

    Presents an oscillation criteria for the first order nonlinear delay differential equation. Theorems for the equations; Main results; Lemmas and proofs to obtain the main results.

  • Split second? Jha, Ramanand // Nature;9/30/1993, Vol. 365 Issue 6445, p398 

    Points out the differential delays in the start procedure of Olympic track events. Sound signal from loudspeakers; Lane width and athlete positions.

  • THE NUMERICAL STABILITY OF THE 0-METHOD FOR DELAY DIFFERENTIAL EQUATIONS WITH MANY VARIABLE DELAYS. Lin Qiu; Mitsui, Taketomo; Jiao-xun Kuang // Journal of Computational Mathematics;Sep99, Vol. 17 Issue 5, p523 

    Discusses the numerical stability of the theta-method for delay differential equations (DDE) with many variable delays. Definitions of a stable numerical method for DDE; Asymptotic stability of the theoretic solution of DDE; Numerical stability of the linear theta-method.

  • Qualitative Behavior of Solutions of Second Order Differential Equations. Cesarano, Clemente; Bazighifan, Omar // Symmetry (20738994);Jun2019, Vol. 11 Issue 6, p777 

    In this work, we study the oscillation of second-order delay differential equations, by employing a refinement of the generalized Riccati substitution. We establish a new oscillation criterion. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study...

  • An ultrasonic system for the inspection of components with irregular geometry using a flexible phased array contact transducer and related processing algorithms. Chatillon, S.; Cattiaux, G.; Serre, M.; Roy, O. // AIP Conference Proceedings;2000, Vol. 509 Issue 1, p1095 

    Contact ultrasonic nondestructive testing of pieces of irregular geometry faces several difficulties: sensitivity losses due to unmatched contact, inaccurate localization of defects due to transducer disorientation, uncovered scan area in the component. We propose a new concept of contact phased...

  • Regenerative Model with Delay for the Cutting Process. Part I: Analytical Approach. STĂNESCU, Nicolae-Doru; POPA, Dinel // Romanian Journal of Acoustics & Vibration;2015, Vol. 12 Issue 1, p75 

    This paper makes an analytical approach for the study of a new regenerative model with delay for the cutting processes. The model has two degrees of freedom and the delay is considered for both of them. In addition, in the most general case, the delays are non-linear ones. The analytical study...

  • Differential delay equations in chemical kinetics: Some simple linear model systems. Epstein, Irving R. // Journal of Chemical Physics;2/1/1990, Vol. 92 Issue 3, p1702 

    The reasons for and the effects of incorporating time lags into the differential equations of chemical kinetics are investigated for some simple model systems. Complex networks of first-order reactions may, in the limit of long times, be described by relatively simple systems of differential...

  • Temperature Properties of Plate Modes in Quartz. Anisimkin, I. V.; Anisimkin, V. I.; Gulyaev, Yu. V.; Verona, E. // Acoustical Physics;Jan2002, Vol. 48 Issue 1, p8 

    The shear horizontal modes that occur in a quartz plate are studied both theoretically and experimentally. These modes are shown to possess a wide variety of temperature properties, including the characteristic behavior of the temperature coefficient of delay, which can take on negative, zero...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics