Consider the scalar nonlinear delay differential equationddt[x(t)-f(t,x(t-τ))]+g(t,x(t-δ))=0,tt 0,where τ,δ(0,∞),f,gC([t 0,∞)×R,R)and xg(t,x)0 for tt 0,x∈R.The author obtains sufficient conditions for the ...Consider the scalar nonlinear delay differential equationddt[x(t)-f(t,x(t-τ))]+g(t,x(t-δ))=0,tt 0,where τ,δ(0,∞),f,gC([t 0,∞)×R,R)and xg(t,x)0 for tt 0,x∈R.The author obtains sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable.展开更多
Based on the primitive equations of the atmosphere,we study the effects of external forcing. dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.The results show that the asymp...Based on the primitive equations of the atmosphere,we study the effects of external forcing. dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.The results show that the asymptotic behavior of solutions of the forced dissipative nonlinear system is essentially different from that of the adiabatic non-dissipative system,the adiabatic dissipative system,the diabatic non-dissipative system and the diabatic dissipative linear system,and that the joint action of external forcing,dissipation and nonlinearity is the source of multiple equilibria. From this we can conclude that the important actions of diabatic heating and dissipation must be considered in the models of the long-term weather and the climate.展开更多
The main purpose of this paper is to analyze the asymptotic behavior of the radial solution of Hénon equation ?Δu = |x| α u p?1, u > 0, x ∈ B R (0) ? ? n (n ? 3), u = 0, x ∈ ?B R (0), where $ p \to p(\alph...The main purpose of this paper is to analyze the asymptotic behavior of the radial solution of Hénon equation ?Δu = |x| α u p?1, u > 0, x ∈ B R (0) ? ? n (n ? 3), u = 0, x ∈ ?B R (0), where $ p \to p(\alpha ) = \frac{{2(n + \alpha )}} {{n - 2}} $ from left side, α > 0.展开更多
This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long time...This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long timescale O(\epsilon\(-1)). As an application of the asymptotic theory, the initial value problems for a special telegraph equation are studied and two asymptotic solutions of order O(\epsilon\(-)1) are presented.展开更多
Consider the following equationwhere 6, c and τ are constants, and τ > 0, bc ≠ 0. In this paper, we establish a necessary and sufficient condition for zero solution of Eq.(*) to be asymptotically stable, which i...Consider the following equationwhere 6, c and τ are constants, and τ > 0, bc ≠ 0. In this paper, we establish a necessary and sufficient condition for zero solution of Eq.(*) to be asymptotically stable, which is easy to verify and apply.展开更多
We prove the global existence and uniqueness of admissible weak solutions to an asymptotic equation of a nonlinear hyperbolic variational wave equation with nonnegative L^2(R) initial data.
In this paper we investigate the boundedness, persistence and asymptoticbehavior of the positive solution of the equation xn+1 = f(xn , xn- 1,… , xn-k)and its special cases.
The authors study the asymptotic behaviour of solutions of the heat equation and a number of evolution equations using scaling techniques. It is proved that in the framework of bounded data stabilization need not occu...The authors study the asymptotic behaviour of solutions of the heat equation and a number of evolution equations using scaling techniques. It is proved that in the framework of bounded data stabilization need not occur and the general asymptotic behaviour is complex. This behaviour reflects for large times, even on compact sets, the complexity of the initial data at infinity.展开更多
MANY dynamic population models can be transformed to the form of delay differential equationx（t） + λx（t） + f（t,x（t-τ<sub>1</sub>）,….,x（t-τ<sub>m</sub>））=0,t≥0,（1）where the biol...MANY dynamic population models can be transformed to the form of delay differential equationx（t） + λx（t） + f（t,x（t-τ<sub>1</sub>）,….,x（t-τ<sub>m</sub>））=0,t≥0,（1）where the biologically meaningful equilibrium of the original equation is transformed into thezero equilibriurn of （1）. Throughout this note, we assume that λ】0,τ<sub>i</sub>】0（i=1,…,m ）,展开更多
In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asy...In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated.展开更多
Consider the first order neutral equations with variable coefficients and several deviations of the form The asymptotic behavior of nonoscillatory solutions of the equations is discussed.Necessary and sufficient condi...Consider the first order neutral equations with variable coefficients and several deviations of the form The asymptotic behavior of nonoscillatory solutions of the equations is discussed.Necessary and sufficient conditions and several sufficient conditions are obtained for aIl solutions of the equations to be oscillatory.展开更多
The boundary value problem for the nonlinear elliptic equation is considered. The outer solution for the original problem is obtained. The boundary and interior layer correction terms are constructed by introducing st...The boundary value problem for the nonlinear elliptic equation is considered. The outer solution for the original problem is obtained. The boundary and interior layer correction terms are constructed by introducing stretched variables and setting local coordinate systems near the boundary and interior discontinuous point of outer solution. Under suitable conditions, using the differential inequalities and the mean value theorem, the existence of the shock solution for boundary value problem is proved and the asymptotic behavior of the solution is studied.展开更多
We consider the existence, both locally and globally in time, as well as the asymptotic behavior of solutions for the Cauchy problem of the sixth-order Boussinesq equation with damping term. Under rather mild conditio...We consider the existence, both locally and globally in time, as well as the asymptotic behavior of solutions for the Cauchy problem of the sixth-order Boussinesq equation with damping term. Under rather mild conditions on the nonlinear term and initial data, we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the problem is globally well-posed.Finally, under certain conditions, we prove that the global solution decays exponentially to zero in the infinite time limit.展开更多
文摘Consider the scalar nonlinear delay differential equationddt[x(t)-f(t,x(t-τ))]+g(t,x(t-δ))=0,tt 0,where τ,δ(0,∞),f,gC([t 0,∞)×R,R)and xg(t,x)0 for tt 0,x∈R.The author obtains sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable.
基金This work was supported by the State Key Research Project on Dynamics and Predictive Theory of the Climate
文摘Based on the primitive equations of the atmosphere,we study the effects of external forcing. dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.The results show that the asymptotic behavior of solutions of the forced dissipative nonlinear system is essentially different from that of the adiabatic non-dissipative system,the adiabatic dissipative system,the diabatic non-dissipative system and the diabatic dissipative linear system,and that the joint action of external forcing,dissipation and nonlinearity is the source of multiple equilibria. From this we can conclude that the important actions of diabatic heating and dissipation must be considered in the models of the long-term weather and the climate.
基金supported by National Natural Science Foundation of China (Grant No. 10631030)the Program for New Century Excellent Talents in University (Grant No. 07-0350)+1 种基金the Key Project of ChineseMinistry of Education (Grant No. 107081)the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Chinese Ministry of Education
文摘The main purpose of this paper is to analyze the asymptotic behavior of the radial solution of Hénon equation ?Δu = |x| α u p?1, u > 0, x ∈ B R (0) ? ? n (n ? 3), u = 0, x ∈ ?B R (0), where $ p \to p(\alpha ) = \frac{{2(n + \alpha )}} {{n - 2}} $ from left side, α > 0.
文摘This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long timescale O(\epsilon\(-1)). As an application of the asymptotic theory, the initial value problems for a special telegraph equation are studied and two asymptotic solutions of order O(\epsilon\(-)1) are presented.
基金The work is supported by Natural Science Foundation of Heilongjiang Province of China, A0207.
文摘Consider the following equationwhere 6, c and τ are constants, and τ > 0, bc ≠ 0. In this paper, we establish a necessary and sufficient condition for zero solution of Eq.(*) to be asymptotically stable, which is easy to verify and apply.
基金The work of Ping Zhang is supported by the Chinese postdoctor's foundation,and that of Yuxi Zheng is supported in part by NSF DMS-9703711 and the Alfred P.Sloan Research Fellows award
文摘We prove the global existence and uniqueness of admissible weak solutions to an asymptotic equation of a nonlinear hyperbolic variational wave equation with nonnegative L^2(R) initial data.
文摘In this paper we investigate the boundedness, persistence and asymptoticbehavior of the positive solution of the equation xn+1 = f(xn , xn- 1,… , xn-k)and its special cases.
文摘The authors study the asymptotic behaviour of solutions of the heat equation and a number of evolution equations using scaling techniques. It is proved that in the framework of bounded data stabilization need not occur and the general asymptotic behaviour is complex. This behaviour reflects for large times, even on compact sets, the complexity of the initial data at infinity.
文摘MANY dynamic population models can be transformed to the form of delay differential equationx（t） + λx（t） + f（t,x（t-τ<sub>1</sub>）,….,x（t-τ<sub>m</sub>））=0,t≥0,（1）where the biologically meaningful equilibrium of the original equation is transformed into thezero equilibriurn of （1）. Throughout this note, we assume that λ】0,τ<sub>i</sub>】0（i=1,…,m ）,
基金supported by National Natural Science Foundation of China (Grant Nos.10671038,10801039)Youth Science Foundation of Fudan University (Grant No.08FQ29)Shanghai Leading Academic Discipline Project (Grant No.B118)
文摘In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated.
文摘Consider the first order neutral equations with variable coefficients and several deviations of the form The asymptotic behavior of nonoscillatory solutions of the equations is discussed.Necessary and sufficient conditions and several sufficient conditions are obtained for aIl solutions of the equations to be oscillatory.
基金Supported by the National Natural Science Foundation of China (40876010)the LASG State Key Laboratory Special Fund of China+3 种基金the Foundation of E-Institutes of Shanghai Municipal Education Commission (E03004)the Foundation of the Education Department of Fujian Province (JA10288)the Natural Science Foundation of Zhejiang Province (Y6090164)the Natural Science Foundation of the Education Bureau of Anhui Province (KJ2011A135)
文摘The boundary value problem for the nonlinear elliptic equation is considered. The outer solution for the original problem is obtained. The boundary and interior layer correction terms are constructed by introducing stretched variables and setting local coordinate systems near the boundary and interior discontinuous point of outer solution. Under suitable conditions, using the differential inequalities and the mean value theorem, the existence of the shock solution for boundary value problem is proved and the asymptotic behavior of the solution is studied.
文摘We consider the existence, both locally and globally in time, as well as the asymptotic behavior of solutions for the Cauchy problem of the sixth-order Boussinesq equation with damping term. Under rather mild conditions on the nonlinear term and initial data, we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the problem is globally well-posed.Finally, under certain conditions, we prove that the global solution decays exponentially to zero in the infinite time limit.
