OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)))g(x′(t))=0are obtained.

Oscillation for Solutions of Systems of High Order Partial Differential Equations of Neutral Type

In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.

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.

The Unconditional Stability for the Multigroup Multidelays Neutral Type Linear Constant Control System

Applying the frequency domain method and the inequality method, we discussed the unconditional stability problem of the multigroup multidelays neutral type linear constant continuous control system, and obtained some sufficient conditions.

2T-PERIODIC SOLUTION FOR m ORDER NEUTRAL TYPEDIFFERENTIAL EQUATIONS WITH TIME DELAYS

Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied. Existence and uniqueness of 2 T-periodic solutions for the equation were discussed by using the method of Fourier series. Some new necessary and sufficient conditions of existence and uniqueness of 2 T-periodic solutions for the equation are obtained. The main result is used widely. It contains results in some correlation paper for its special case, improves and extends the main results in them. Existence of periodic solution for the equation in larger number of particular case can be checked by using the result, but cannot be checked in another paper. In other words, the main result in this paper is most generalized for (1) the better result cannot be found by using the same method.

Asymptotical Properties for Parabolic Systems of Neutral Type

Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis.The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.

Remarks on Oscillation for Systems of High Order Partial Differential Equations of Neutral Type

In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.

Periodic Solution for Neutral Type Neural Networks

The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.

On the decomposition problem of neutral type linear large scale control system in the theory of stabilization(1)

In this paper we choose the symmetric positive definite solutionof Riccati matrix algebraic equation and,construct a positive defini-tequadratic form V-function and,use Lyapunov deco mpositionequivalence method founded by Liu Yong-qing to obtain the condi-tions of the asymptotic stability of the solution of neutral typelinear large scale control system,the estimate formula of thedecom posing coefficients and time delay are also given.

Oscillation of Solutions of Nonlinear Partial Differential Equations of Neutral Type

In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j(u(x,σ_j(t))) =a(t)△u(x,t)+sun form k=1 to n ak(t)△u(x,pk(t)), (x,t)∈Ω×R_+≡G where △ is the Laplacian in Euclidean N-space R^N, R_+=(0, ∞) and Ω is a bounded domain in R^N with a piecewise smooth boundary Ω.

OSCILLATION OF HYPERBOLIC DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

Neutral hyperbolic differential equations with continuous distributed devia-ting arguments are studied, and sufficient conditions for each solution of the boundary value problem to be oscillatory in a cylindrical domain are obtained.

Global Exponential Convergence of Neutral Type Competitive Neural Networks with D Operator and Mixed Delay

The models of competitive neural network(CNN)was in recent past proposed to describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications,where there are two types of memories:Long-term memories(LTM)and short-term memories(STM),LTM presents unsupervised and slow synaptic modifications and STM characterize the fast neural activity.This paper is concerned with a class of neutral type CNN’s with mixed delay and D operator.By employing the appropriate differential inequality theory,some sufficient conditions are given to ensure that all solutions of the model converge exponentially to zero vector.Finally,an illustrative example is also given at the end of this paper to show the effectiveness of the proposed results.

OSCILLATION CRITERIA FOR SECOND ORDER DIFFERENCE EQUATIONS OF NEUTRAL TYPE WITH MIXED ARGUMENTS

In this paper, we establish some new oscillation criteria for second order difference equations of neutral type with mixed arguments. We extend some known oscillation criteria for second order difference equations.

OSCILLATION OF THE SOLUTION TO NONLINEAR PARABOLIC DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

Sufficient conditions are obtained for the oscillation of the solutions to nonlinear parabolic differential equations of neutral type in the form of where Ω is a bounded domain in Rn with a piecewise smooth boundary.

Existence of Periodic Solutions for Neutral-Type Neural Networks with Delays on Time Scales

In this paper, we employ a fixed point theorem due to Krasnosel’skii to attain the existence of periodic solutions for neutral-type neural networks with delays on a periodic time scale. Some new sufficient conditions are established to show that there exists a unique periodic solution by the contraction mapping principle.

Stability of solutions to neutral type parabolic systemswith time delay

On the study of the solutions to the partial functional differential equations,there existsome good results.However,for the related neutral-type systems,there seems to be noresult appearing to deal with the stability of solutions due to the difficulties of study.In this note,we will make some explorations by constructing several auxillary functionalsand combining L_p-estimates to analyze the stability of solutions to a class of

RAZUMIKHIN-TYPE THEOREMS OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.

RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.

Three amino acid residues in the envelope of human immunodeficiency virus type 1 CRF07_BC regulate viral neutralization susceptibility to the human monoclonal neutralizing antibody IgG1b12

The CD4 binding site(CD4bs) of envelope glycoprotein(Env) is an important conserved target for anti-human immunodeficiency virus type 1(HIV-1) neutralizing antibodies. Neutralizing monoclonal antibodies IgG1 b12(b12) could recognize conformational epitopes that overlap the CD4 bs of Env. Different virus strains, even derived from the same individual, showed distinct neutralization susceptibility to b12. We examined the key amino acid residues affecting b12 neutralization susceptibility using single genome amplification and pseudovirus neutralization assay. Eleven amino acid residues were identified that affect the sensitivity of Env to b12. Through site-directed mutagenesis, an amino acid substitution at position 182 in the V2 region of Env was confirmed to play a key role in regulating the b12 neutralization susceptibility. The introduction of V182 L to a resistant strain enhanced its sensitivity to b12 more than twofold. Correspondingly, the introduction of L182 V to a sensitive strain reduced its sensitivity to b12 more than tenfold. Amino acid substitution at positions 267 and 346 could both enhance the sensitivity to b12 more than twofold. However, no additive effect was observed when the three site mutageneses were introduced into the same strain, and the sensitivity was equivalent to the single V182 L mutation. CRF07_BC is a major circulating recombinant form of HIV-1 prevalent in China. Our data may provide important information for understanding the molecular mechanism regulating the neutralization susceptibility of CRF07_BC viruses to b12 and may be helpful for a vaccine design targeting the CD4 bs epitopes.