一类时滞微分系统的周期解

研究了一类具分布时滞的一阶微分系统的周期解的存在性和全局吸引性.先通过利用重合度理论中的Mawhin延拓定理讨论了周期解的存在性,建立了一些判断准则;进而通过构造适当的Lyapunov泛函以及周期解的存在性结果研究了该类时滞微分系统的周期解的全局吸引性,获得了保证其周期解全局吸引的充分性条件.     

一类带时滞和全局反应项生物模型的行波解

研究了带时滞的微分方程异宿轨解的存在条件,并通过时滞微分系统和反应扩散系统解之间的关联性,得到了一类带全局反应项的生物反应扩散模型的行波解.     

具有源项的等熵气体动力学方程组全局解的存在性

本文我们证明了具有源项的等熵气体动力学方程组(1.2)全局解的存在性.为此,我们构造正则双曲方程组(1.1)去逼近非齐次等熵气体动力学方程组(1.2).首先,对每一个固定的逼近参数δ和一般化的P(ρ)条件,我们证明了带有界初始条件(1.4)的Cauchy问题(1.1)的全局熵解的存在性.其次,令∈=o(δ),我们得到了方程组(1.2)的形如η(ρ,u)=ρH(ρ,u)(与Chen和LeFloch(2003)相同)的弱熵对的H_(loc)~(-1)紧性的完整证明.最后,将Chen和LeFloch(2003)给出的关于P(ρ)的条件应用到定理1和定理2的结果中,我们得到了带有界初值(1.4)的Cauchy问题(1.2)的熵解的全局存在性.     

Hopfield神经网络概周期解的存在性和全局吸引性

该文研究Ｈｏｐｆｉｅｌｄ神经网络概周期解的存在性和全局吸性,获得了该网络存在唯一概周期解的充分条件和所有解收敛于此概周期解的充分条件。     

退缩抛物方程组解的全局存在性

利用上下解方法讨论一类退缩抛物方程组存在全局解的条件,并证明了在一定条件下全局解的收敛性.     

带有次线性项和超线性项的Klein-Gordon-Maxwell系统多重解的存在性

该文研究如下Klein-Gordon-Maxwell系统■多重解的存在性,其中4p6,1q2,λ0.在a(x)、b(x)、参数λ满足一定的假设条件下,通过变分方法证明了系统无穷解的存在性.补充和完善了以上方程解存在性的以往结果.     

一类微分方程零解全局弱吸引和全局吸引到充要条件

考虑二阶微分方程 x =φ(y)-F(x),y=- g(x)q(y) 零解的全局弱吸引和全局吸引性, 说明了Filippov条件(A₂) 不能排除最大椭圆扇形S^* 的存在性, 也不能排除∂S^* 作为其外侧邻域轨线正向极限集的可能. 全面回答了文献[8]末提出的问题;得到了方程(E)满足或不满足Filippov 条件时零解全局弱吸引和全局吸引的一系列充分必要条件, 同时也得到了零解全局渐近稳定的一些新条件.     

一类无穷时滞微分系统的周期解和全局渐近稳定性

利用重合度理论中的延拓定理和微分不等式讨论一类无穷时滞微分系统的周期解的存在性和全局渐近稳定性,获得了简便的判别条件.     

Robin边界条件下更一般化的非线性抛物问题全局解的存在性和爆破

本文主要研究了Robin边界条件下更一般化的非线性抛物问题解的爆破现象以及全局解的存在性.通过对问题中的已知函数进行适当的假设,建立适当的辅助函数,应用微分不等式技术,当问题的解发生爆破时得到了解的爆破时间的下界.这种类型的下界在物理学、生物学、天文学等领域有着广泛的应用.同时,也推导了问题的解全局存在的条件.     

一类BAM神经网络的概周期解的存在性和指数收敛性

利用不动点理论和推广的Halanay时滞微分不等式,研究一类双向联想记忆神经网络的概周期解的存在性和全局指数收敛性,给出其判定的充分性条件.     

Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions

This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions.For the heat diffusion case,the necessary and sufficient conditions on the global existence of all positive solutions are obtained.For the general fast diffusion case,we get some conditions on the global existence and nonexistence of positive solutions.The results of this paper fill the some gaps which were left in this field.     

Global well-posedness for semilinear hyperbolic equations with dissipative term

We study the initial boundary value problem of semilinear hyperbolic equations with dissipative term. By introducing a family of potential wells we derive the invariant sets and vacuum isolating of solutions. Then we prove the global existence, nonexistence and asymptotic behaviour of solutions. In particular we obtain some sharp conditions for global existence and nonexistence of solutions.     

On the nonexistence of global solutions of the Hamilton-Jacobi equation

Although examples of nonexistence of global solutions of Hamilton-Jacobi equations have long been known, the general theory of nonexistence of global solutions (unlike the general theory of existence of global viscous solutions) does not yet exist.In the present paper, we use examples of model Hamilton-Jacobi equations to demonstrate how simple methods for the analysis of the problem of nonexistence of global solutions (in the corresponding function class) can be applied.     

Closing the gap in the purely elliptic generalized Davey–Stewartson system

In this note we improve the results presented previously on global existence and global nonexistence for the solutions of the purely elliptic generalized Davey–Stewartson system. These results left a gap in the parameter range where neither a global existence result nor a global nonexistence result could be established. Here we are able to show that when the coupling parameter is negative there is no gap. Moreover, in the case where the coupling parameter is positive we reduce the size of the gap.     

Existence and nonexistence of global positive solutions for a weakly coupled P-Laplacian system

In this paper, we deal with a weakly coupled evolution P-Laplacian system with inhomogeneous terms. We obtain a critical criterion concerning existence and nonexistence of its global positive solutions. Such a criterion is different from that of the weakly coupled evolution P-Laplacian system with homogeneous terms. Further, we demonstrate existence and nonexistence of its global positive solutions.     

Doubly Nonlinear Degenerate Parabolic Systems with Coupled Nonlinear Boundary Conditions

In this paper, we study the global existence and the global nonexistence of doubly nonlinear degenerate parabolic systems with nonlinear boundary conditions. We first prove a local existence result by the regularization method. Next, we construct a weak comparison principle. Then we discuss the large time behavior of solutions by using a modified upper and lower solution methods and constructing various upper and lower solutions. Necessary and sufficient conditions on the global existence of all positive (weak) solutions are obtained.     

Global existence,nonexistence and asymptotic behavior of solutions for the Cauchy problem of semilinear heat equations

In this paper, we study the Cauchy problem of semilinear heat equations. By introducing a family of potential wells, we first prove the invariance of some sets and isolating solutions. Then we obtain a threshold result for the global existence and nonexistence of solutions. Finally we discuss the asymptotic behavior of the solution.     

On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources

In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||_f||| _h and 〈f〉_h, we give the sufficient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered. This work was supported by the National Natural Science Foundation of China (Grant No. 10531020)     

奇异半线性热方程初值问题解的存在性与Blow-up问题

本文讨论如下奇异半线性热方程的初值问题其中γ＞1，σ＞O，f（x）连续有界非负但不恒为零．我们讨论了问题（1），（2）非负局部经典解的存在性和非负整体解的不存在问题，得到当0＜σ＜1且时，（1），（2）没有非负整体解．当σ＝1且时，（1），（2）没有非负整体解，当σ＞1时（1），（2）没有非负整体解．     

一类退化抛物方程解的存在唯一性及爆破速率

本文运用正则化方法证明了一类退化抛物方程解的存在唯一性,讨论了解的全局存在性与爆破,并在一定的初值条件下得到了解的爆破速率.