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LOCAL BIFURCATION OF STEADY ALMOST PERIODIC WATER WAVES WITH CONSTANT VORTICITY
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作者 罗巍 殷朝阳 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1633-1644,共12页
In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed.We assume that the free surface is almost periodic in the horizontal dir... In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed.We assume that the free surface is almost periodic in the horizontal direction.Using conformal mappings,one can change the free boundary problem into a fixed boundary problem for some unknown functions with the boundary condition.By virtue of the Hilbert transform,the problem is equivalent to a quasilinear pseudodifferential equation for an almost periodic function of one variable.The bifurcation theory ensures that we can obtain an existence result.Our existence result generalizes and covers the recent result in[15].Moreover,our result implies a non-uniqueness result at the same bifurcation point. 展开更多
关键词 water waves almost periodic functions bifurcation theory constant vorticity
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Mean-square Almost Periodic Random Functions
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作者 江利娜 张传义 《Northeastern Mathematical Journal》 CSCD 2007年第3期215-225,共11页
In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equat... In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation. 展开更多
关键词 mean-square convergence mean-square almost periodic random function Ito integration
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Pseudo Almost Periodic Solutions of Nonlinear Hyperbolic Equations with Piecewise Constant Argument 被引量:1
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作者 周红燕 朴大雄 《Northeastern Mathematical Journal》 CSCD 2007年第6期491-504,共14页
In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model... In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model for the dynamics of gas absorption, 展开更多
关键词 uniformly almost periodic function uniformly pseudo almost periodicfunction uniformly almost periodic sequence uniformly pseudo almost periodic se-quence fixed point Method
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Pseudo Almost Periodic Solutions for Second Order Abstract Differential Equations
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作者 谢灵红 顾晓慧 谢建华 《Journal of Southwest Jiaotong University(English Edition)》 2003年第1期98-102,共5页
On the assumption that the Cauchy problem for incomplete second order abstract differential equation (u″(t)=Au(t), -∞ <t <∞) is well posed and the Cauchy problem for complete second order abstract diff... On the assumption that the Cauchy problem for incomplete second order abstract differential equation (u″(t)=Au(t), -∞ <t <∞) is well posed and the Cauchy problem for complete second order abstract differential equation ( u″(t)+A 1u′(t)+A 0u(t)=0, t≥0 ) is strongly well posed, the necessary conditions for their solutions to be pseudo almost periodic are derived. 展开更多
关键词 pseudo almost periodic function second order abstract differential equation Cauchy problem necessary conditions
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ASYMPTOTICALLY ALMOST PERIODIC FUNCTIONS IN PROBABILITY
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作者 Yuliang Han Baifeng Liu +1 位作者 Xidong Sun Xiliang Li 《Annals of Differential Equations》 2013年第1期17-24,共8页
In this paper, we first study the properties of asymptotically almost periodic functions in probability and then prove the existence of almost periodic solutions in probability to some differential equations with rand... In this paper, we first study the properties of asymptotically almost periodic functions in probability and then prove the existence of almost periodic solutions in probability to some differential equations with random terms. 展开更多
关键词 almost periodic functions in probability asymptotically almost periodic functions in probability
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STABILITY AND ALMOST PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY 被引量:1
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作者 袁荣 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1998年第1期68-73,共6页
For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if perio... For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to then Eq.(1) has an mω-periodic solution p(t), for some integer m≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq.(1) has an almost periodic solution. 展开更多
关键词 almost periodic solutions stability with respect to hull neutral functional differential equations infinite delay
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PSEUDO ALMOST PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITHPIECEWISE CONSTANT ARGUMENT 被引量:11
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作者 PIAODAX10NG YUANRONG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1999年第4期489-494,共6页
The authors discuss the existence of pseudo almost periodic solutions of differential equations with piecewise constant argument by means of introducing new concept, pseudo almost periodic sequence.
关键词 Pseudo almost periodic functions Pseudo almost periodic sequences Piecewise constant arguments Ergodic perturbation
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Pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument [t] 被引量:8
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作者 朴大雄 《Science China Mathematics》 SCIE 2001年第9期1156-1161,共6页
In this paper, we investigate the existence and uniqueness of new almost periodic type solutions, so-called pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument b... In this paper, we investigate the existence and uniqueness of new almost periodic type solutions, so-called pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument by means of introducing the notion of pseudo almost periodic vector sequences. 展开更多
关键词 pseudo almost periodic functions pseudo almost periodic sequences piecewise constant arguments ergodic perturbation.
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Almost Periodic Solutioiis of Neutral Differential Difference Equations with Piecewise Constant Arguments 被引量:3
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作者 PIAO Da Xiong Department of Mathematics,Fushun Petroleum Institute.Fushun 113001,P.R.China E-mail:piaodx@fspu.edu.cn 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2002年第2期263-276,共14页
In this paper,we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.
关键词 almost periodic functions almost periodic sequences Piecewise constant arguments Neutral differential difference equations
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