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THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS
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作者 黄先勇 邓勋环 王其如 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期925-946,共22页
In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existe... In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results. 展开更多
关键词 nonlinear delay dynamic equations NONOSCILLATION asymptotic behavior Philostype oscillation criteria generalized Riccati transformation
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ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS 被引量:1
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作者 曾六川 《Acta Mathematica Scientia》 SCIE CSCD 2006年第2期246-254,共9页
This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak conver... This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results. 展开更多
关键词 Semitopological semigroup almost asymptotically nonexpansive type mapping almost orbit asymptotic behavior
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DYNAMICS FOR A CHEMOTAXIS MODEL WITH GENERAL LOGISTIC DAMPING AND SIGNAL DEPENDENT MOTILITY
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作者 涂馨予 穆春来 +1 位作者 邱蜀燕 张静 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期1046-1063,共18页
In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥... In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥1)is a smooth and bounded domain,λ≥0,μ≥0,κ>1,and the motility function satisfies thatγ(v)∈C3([0,∞)),γ(v)>0,γ′(v)≤0 for all v≥0.Considering the Neumann boundary condition,we obtain the global boundedness of solutions if one of the following conditions holds:(i)λ=μ=0,1≤nλ3;(ii)λ>0,μ>0,combined withκ>1,1≤n≤3 or k>n+2/4,,n>3.Moreover,we prove that the solution (u, v, w, z) exponentially converges to the constant steady state ((λ/μ)1/k-1,∫Ωv0dx+∫Ωw0dx/|Ω|,0,(λ/μ)1/k-1). 展开更多
关键词 CHEMOTAXIS signal-dependent motility logistic source boundedness asymptotic behavior
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NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES
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作者 韩月才 张丁文 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期143-160,共18页
We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed proces... We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology. 展开更多
关键词 reflected stochastic differential equation discretely observed process continuously observed process Nadaraya-Watson estimator asymptotic behavior
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NORMALIZED SOLUTIONS FOR THE GENERAL KIRCHHOFF TYPE EQUATIONS
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作者 Wenmin LIU Xuexiu ZHONG Jinfang ZHOU 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1886-1902,共17页
In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈ℝ×H^(1)(ℝ^(N))to the general Kirchhoff problem-M\left(\int_{\mathbb{R}^N}\vert\nabla u\ve... In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈ℝ×H^(1)(ℝ^(N))to the general Kirchhoff problem-M\left(\int_{\mathbb{R}^N}\vert\nabla u\vert^2{\rm d}x\right)\Delta u+\lambda u=g(u)~\hbox{in}~\mathbb{R}^N,u\in H^1(\mathbb{R}^N),N\geq 1,satisfying the normalization constraint\int_{\mathbb{R}^N}u^2{\rm d}x=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical. 展开更多
关键词 normalized solution Kirchhoff type equations general nonlinearities asymptotic behavior
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A SINGULAR DIRICHLET PROBLEM FOR THE MONGE-AMPÈRE TYPE EQUATION
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作者 Zhijun ZHANG Bo ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1965-1983,共19页
We consider the singular Dirichlet problem for the Monge-Ampère type equation{\rm det}\D^2 u=b(x)g(-u)(1+|\nabla u|^2)^{q/2},\u<0,\x\in\Omega,\u|_{\partial\Omega}=0,whereΩis a strictly convex and bounded smoo... We consider the singular Dirichlet problem for the Monge-Ampère type equation{\rm det}\D^2 u=b(x)g(-u)(1+|\nabla u|^2)^{q/2},\u<0,\x\in\Omega,\u|_{\partial\Omega}=0,whereΩis a strictly convex and bounded smooth domain inℝn,q∈[0,n+1),g∈C∞(0,∞)is positive and strictly decreasing in(0,∞)with\lim\limits_{s\rightarrow 0^+}g(s)=\infty,and b∈C∞(Ω)is positive inΩ.We obtain the existence,nonexistence and global asymptotic behavior of the convex solution to such a problem for more general b and g.Our approach is based on the Karamata regular variation theory and the construction of suitable sub-and super-solutions. 展开更多
关键词 Monge-Ampère equation a singular boundary value problem the unique convex solution global asymptotic behavior
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Asymptotic Behavior and Nonexistence of Positive Solutions of Delay Difference Equations *L
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作者 彭名书 徐千里 《Journal of Beijing Institute of Technology》 EI CAS 1999年第1期25-30,共6页
Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some i... Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included. 展开更多
关键词 OSCILLATION asymptotic behavior positive solution neutral delay difference equation NONLINEARITY
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ASYMPTOTIC BEHAVIOR OF SOLUTION FOR NONLOCAL REACTION-DIFFUSION SYSTEM 被引量:8
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作者 栗付才 陈有朋 谢春红 《Acta Mathematica Scientia》 SCIE CSCD 2003年第2期261-273,共13页
This paper deals with reaction-diffusion system with nonlocal source. It is proved that there exists a unique classical solution and the solution either exists globally or blows up in finite time. Furthermore, its blo... This paper deals with reaction-diffusion system with nonlocal source. It is proved that there exists a unique classical solution and the solution either exists globally or blows up in finite time. Furthermore, its blow-up set and asymptotic behavior are obtained provided that the solution blows up in finite time. 展开更多
关键词 Nonlocal source global existence BLOW-UP blow-up set asymptotic behavior of solution
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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR THE 3D COMPRESSIBLE NON–ISENTROPIC EULER EQUATIONS WITH DAMPING 被引量:4
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作者 张映辉 吴国春 《Acta Mathematica Scientia》 SCIE CSCD 2014年第2期424-434,共11页
We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical s... We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods. 展开更多
关键词 Euler equations with damping global existence asymptotic behavior
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COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION 被引量:3
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作者 尹景学 王良伟 黄锐 《Acta Mathematica Scientia》 SCIE CSCD 2010年第6期1865-1880,共16页
In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um + yup = 0,where γ≥0,m〉 1and P〉m+2/N We will show that if γ... In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um + yup = 0,where γ≥0,m〉 1and P〉m+2/N We will show that if γ=0 and 0〈μ〈 2N/n(m-1)+2 or γ 〉 0 and 1/p-1 〈 μ 〈 2N/N(m-1)+2 then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S(RN), there exists an initial-value u0 ∈ C(RN) with limx→∞ uo(x)= 0 such that φ is an w-limit point of the rescaled solutions tμ/2u(tβ, t), Where β = 2-μ(m-1)/4. 展开更多
关键词 COMPLEXITY asymptotic behavior porous medium equation
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LARGE TIME BEHAVIOR OF SOLUTIONS TO1-DIMENSIONAL BIPOLAR QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS 被引量:2
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作者 李杏 雍燕 《Acta Mathematica Scientia》 SCIE CSCD 2017年第3期806-835,共30页
In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this... In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this kind of model in one dimensional case for general perturbations by constructing some correction functions to delete the gaps between the original solutions and the diffusion waves in L2-space, and by using a key inequality we prove the stability of diffusion waves. As the same time, the convergence rates are also obtained. 展开更多
关键词 Bipolar quantum hydrodynamic diffusion waves semiconductor Euler-Poissoneuqations asymptotic behavior
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ASYMPTOTIC BEHAVIOR FOR A CLASS OF ELLIPTICEQUIVALUED SURFACE BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS INTERFACE CONDITIONS 被引量:6
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作者 CAI ZHIJIE(Institute of Mathematics, Fudan University, Shanghai 200433.) 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1995年第3期237-250,共14页
Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies an elliptic equivalued surface boundary value problem with discontinuous interface con... Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies an elliptic equivalued surface boundary value problem with discontinuous interface conditions. In practice, the measuring electrode is so small that we can simplify the corresponding equivalued surface to a point. In this paper, we give a positive answer to this approximation process:when the equivalued surface shrinks to a point, the solution of the original equivalued surface boundary value problem converges to the solution of the corresponding limit boundary value problem. 展开更多
关键词 Spontaneous potential well-logging equivalued surface boundary value problem asymptotic behavior
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On the Asymptotic Behavior of Certain Second Order Differential Equations 被引量:3
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作者 XUZhi-ting XIAYong 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第2期186-187,共2页
Two criteria for asymptotic behavior of certain second order differential equations are obtained. The results extend and improve Feng's theorem.
关键词 asymptotic behavior second order differential equation BOUNDED
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ASYMPTOTIC BEHAVIOR OF LINEAR ADVANCED DIFFERENTIAL EQUATIONS 被引量:2
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作者 Nguyen Tien DUNG 《Acta Mathematica Scientia》 SCIE CSCD 2015年第3期610-618,共9页
In this article, we consider a general class of linear advanced differential equa- tions, and obtain explicitly sufficient conditions of convergence and exponential convergence to zero. A necessary condition is provid... In this article, we consider a general class of linear advanced differential equa- tions, and obtain explicitly sufficient conditions of convergence and exponential convergence to zero. A necessary condition is provided as well. 展开更多
关键词 Advanced differential equations asymptotic behaviors fixed points
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Asymptotic Behavior of a Stochastic SIRS Model with Non-linear Incidence and Levy Jumps 被引量:2
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作者 臧彦超 李俊平 《Journal of Donghua University(English Edition)》 EI CAS 2014年第3期217-223,共7页
A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ulti... A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model. 展开更多
关键词 susceptible-infective-recovered-susceptible(SIRS) epidemic model Levy noise stochastic ultimate boundedness asymptotic behavior
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ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS 被引量:1
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作者 汤燕斌 周笠 Omer Ali 《Acta Mathematica Scientia》 SCIE CSCD 2004年第2期307-312,共6页
The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding ste... The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding steady state solutions. Then, the above results are extended to a semilinear parabolic equation with nonlinear boundary condition by analyzing the corresponding eigenvalue problem and using the method of upper and lower solutions. 展开更多
关键词 Asymptotic behavior heat equation nonlinear boundary condition upper and lower solutions
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EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A SINGULAR PARABOLIC EQUATION 被引量:1
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作者 夏莉 李敬娜 姚正安 《Acta Mathematica Scientia》 SCIE CSCD 2012年第5期1875-1882,共8页
In this paper,we study the initial-boundary value problem for a class of singular parabolic equations.Under some conditions,we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regu... In this paper,we study the initial-boundary value problem for a class of singular parabolic equations.Under some conditions,we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method.As a byproduct,we prove the existence of solutions to some problems with gradient terms,which blow up on the boundary. 展开更多
关键词 EXISTENCE singular parabolic equation asymptotic behavior
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EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR A NONLINEAR ELLIPTIC EQUATION ARISING IN ASTROPHYSICS 被引量:1
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作者 唐仲伟 《Acta Mathematica Scientia》 SCIE CSCD 2006年第2期229-245,共17页
The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -△u =φ(r)u^p-1, u 〉 0 in R^N,... The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -△u =φ(r)u^p-1, u 〉 0 in R^N, u ∈ D^1,2(R^N), where N ≥ 3, x = (x^1,z) ∈ R^K×R^N-K,2 ≤ K ≤ N,r = |x′|. It is proved that for 2(N-s)/(N-2) 〈 p 〈 2^* = 2N/(N - 2), 0 〈 s 〈 2, the above equation has a ground state solution and a cylindrically symmetric solution. For p = 2^*, the above equation does not have a ground state solution but a cylindrically symmetric.solution, and when p close to 2^*, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2*, the ground state solution Up has a unique maximum point xp = (x′p, Zp) and as p → 2^*, |x′p| → r0 which attains the maximum of φ on R^N. The asymptotic behavior of ground state solution Up is also given, which also deduces that the ground state solution is not cylindrically symmetric as p goes to 2^*. 展开更多
关键词 Cylindrical symmetry asymptotic behavior ground state solution
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THE ASYMPTOTIC BEHAVIOR AND SYMMETRY OF POSITIVE SOLUTIONS TO p-LAPLACIAN EQUATIONS IN A HALF-SPACE
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作者 Yujuan CHEN Lei WEI Yimin ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第5期2149-2164,共16页
We study a nonlinear equation in the half-space with a Hardy potential,specifically,−Δ_(p)u=λu^(p−1)x_(1)^(p)−x_(1)^(θ)f(u)in T,where Δp stands for the p-Laplacian operator defined by Δ_(p)u=div(∣Δu∣^(p−2)Δu)... We study a nonlinear equation in the half-space with a Hardy potential,specifically,−Δ_(p)u=λu^(p−1)x_(1)^(p)−x_(1)^(θ)f(u)in T,where Δp stands for the p-Laplacian operator defined by Δ_(p)u=div(∣Δu∣^(p−2)Δu),p>1,θ>−p,and T is a half-space{x_(1)>0}.When λ>Θ(where Θ is the Hardy constant),we show that under suitable conditions on f andθ,the equation has a unique positive solution.Moreover,the exact behavior of the unique positive solution as x_(1)→0^(+),and the symmetric property of the positive solution are obtained. 展开更多
关键词 p-Lapacian Hardy potential SYMMETRY UNIQUENESS asymptotic behavior
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Existence and asymptotic behavior for systems of nonlinear hyperbolic equations
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作者 YE Yao-jun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第4期453-465,共13页
The initial-boundary value problem for a class of nonlinear hyperbolic equations system in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obta... The initial-boundary value problem for a class of nonlinear hyperbolic equations system in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obtain the asymptotic stability of global solutions by means of a difference inequality. 展开更多
关键词 Nonlinear hyperbolic equations system global solutions asymptotic behavior difference inequal-ity damping and source terms.
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