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1.
Yaping Liu 《Proceedings of the American Mathematical Society》2005,133(12):3619-3626
The global stability of a multi-species interacting system has apparently important biological implications. In this paper we study the global stability of Gause-type predator-prey models by providing new criteria for the nonexistence of cycles and limit cycles. Our criteria have clear geometrical interpretations and are easier to apply than other methods employed in recent studies. Using these criteria and related techniques we are able to develop new results on the existence and uniqueness of cycles in Gause-type models with various growth and response functions.
2.
给出了下列方程 u″(t) ,(u,t)u′(t) g(u,t)=e(t)边值问题周期解的存在唯一性问题的一些新的判定条件. 相似文献
3.
A. Aghajani 《Journal of Mathematical Analysis and Applications》2007,326(2):1076-1089
We consider the nonlinear Euler differential equation t2x″+g(x)=0. Here g(x) satisfies xg(x)>0 for x≠0, but is not assumed to be sublinear or superlinear. We present implicit necessary and sufficient condition for all nontrivial solutions of this system to be oscillatory or nonoscillatory. Also we prove that solutions of this system are all oscillatory or all nonoscillatory and cannot be both. We derive explicit conditions and improve the results presented in the previous literature. We extend our results to the extended equation t2x″+a(t)g(x)=0. 相似文献
4.
二阶非线性泛函微分方程的振动性质 总被引：1，自引：0，他引：1
研究了一类二阶非线性泛函微分方程解的振动性质.在一定条件下,应用分类讨论和分析的方法,建立了一个新的振动性定理,推广和改进了已知的结果. 相似文献
5.
Giuseppe Di Fazio Pietro Zamboni 《Proceedings of the American Mathematical Society》2002,130(9):2655-2660
In this note we prove a Fefferman-Poincaré type inequality in spaces with metric induced by Carnot-Carathéodory vector fields.
6.
Anatolii Grinshpan 《Proceedings of the American Mathematical Society》2002,130(2):453-460
We analyze a minimum energy problem for a discrete electrostatic model in the complex plane and discuss some applications. A natural characteristic distinguishing the state of minimum energy from other equilibrium states is established. It enables us to gain insight into the structure of positive trigonometric polynomials and Dirichlet spaces associated with finitely atomic measures. We also derive a related family of linear second order differential equations with polynomial solutions.
7.
Given a polynomial with integer coefficients, we calculate the density of the set of primes modulo which the polynomial has a root. We also give a simple criterion to decide whether or not the polynomial has a root modulo every non-zero integer.
8.
给出伪多元函数的Pad'{e}型逼近,其优点在于:简化了多元函数有理逼近的计算,加速了函数在奇点处的收敛.并讨论其性质以及误差分析. 相似文献
9.
Yuan Guangwei 《偏微分方程(英文版)》1994,7(1)
A phase change problem with Joule's heat ing describes tbe processes of electric heating in a conducting material. It is modeled as a coupled system of nonlinear partial differential equations with quadratic growth in the gradient. We establish the existence of a weak solution for the problem in two dimensions. 相似文献
10.
C1,α Regularity of Viscosity Solutions of Fully Nonlinear Parabolic PDE Under Natural Structure Conditions 
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下载免费PDF全文 Ge Han 《偏微分方程(英文版)》1999,12(1):1-10
In this paper, we concern the fully nonlinear parabolic equations u_t + F(x, t , u, Du, D² u) = 0. Under the natural structure conditions as that in [1], we obtain the C^{1,\alpha} estimates of the viscosity solutions. 相似文献
11.
In this paper, we consider a class of Monge-Ampere equations in relative differential geometry. Given these equations with zero boundary values in a smooth strictly convex bounded domain, we obtain second order derivative estimates of the convex solutions. 相似文献
12.
In this paper, we mainly study the number of limit cycles for a quintic Li\"{e}nard system under polynomial perturbations. In some cases, we give new estimations for the lower bound of the maximal number of limit cycles. 相似文献
13.
Mohamed Chraibi Kaadoud 《Proceedings of the American Mathematical Society》2004,132(8):2421-2428
In this paper, we present an extension of Bouldin's result (1970) concerning the numerical range of the product of two operators and that are commuting and for which one of the set or consists of positive numbers. We also prove that if or is a subnormal operator on a separable Hilbert space, then
where is the operator bimultiplication and is the convex hull.
où est l'opérateur produit ou bimultiplication et est l'enveloppe convexe.
where is the operator bimultiplication and is the convex hull.
RÉSUMÉ. Dans ce travail, nous améliorons un résultat de Bouldin (1970) concernant la localisation de le domaine numérique du produit de deux opérateurs et sur un espace de Hilbert lorsque et commutent et est constitué de réels strictement positifs. Dans le cas où ou est un opérateur sous normal sur un espace de Hilbert séparable, nous montrons que
où est l'opérateur produit ou bimultiplication et est l'enveloppe convexe.
14.
In consideration of the important impact of plankton body size and L$acute{e}$vy noise on plankton system, a stochastic phytoplankton-zooplankton system with L$acute{e}$vy jump is proposed and investigated in this paper. Firstly, we prove that there is a unique global positive solution to the system by using Lyapunov function and It$check{o}$ formula. Then, some thresholds which depend on plankton body size are given, and they determine the extinction and weak persistence in the mean of plankton populations. In addition, the sufficient conditions for the existence of a stationary distribution of the solution are given. Finally, some numerical simulations are introduced to support the main theoretical results and illustrate the impact of plankton body size and environmental noise on plankton populations. 相似文献
15.
16.
M. Kon Y. G. Sficas I. P. Stavroulakis 《Proceedings of the American Mathematical Society》2000,128(10):2989-2997
This paper is concerned with the oscillatory behavior of first-order delay differential equations of the form
| (1) |
where is non-decreasing, for and . Let the numbers and be defined by
It is proved here that when and all solutions of Eq. (1) oscillate in several cases in which the condition
2k+frac{2}{{lambda}_{1}}-1 end{displaymath}\">
holds, where is the smaller root of the equation .
17.
Using operator-valued $dot{C}^alpha$-Fourier multiplier results on vector- valued H\"older continuous function spaces, we give a characterization for the $C^alpha$-well-posedness of the first order degenerate differential equations with infinite delay $(Mu)\"(t) = Au(t) + int_{-infty}^t a(t-s)Au(s)ds + f(t)$ ($tinR$), where $A, M$ are closed operators on a Banach space $X$ such that $D(A)cap D(M)neq {0}$, $ain L^1_{rm{loc}}(R_+)cap L^1(mathbb{R}_+; t^alpha dt)$. 相似文献
18.
Although general order multivariate Padé approximants were introduced some decades ago, very few explicit formulas for special functions have been given. We explicitly construct some general order multivariate Padé approximants to the class of so-called pseudo-multivariate functions, using the Padé approximants to their univariate versions. We also prove that the constructed approximants inherit the normality and consistency properties of their univariate relatives, which do not hold in general for multivariate Padé approximants. Examples include the multivariate forms of the exponential and the -exponential functions and as well as the Appell function and the multivariate form of the partial theta function
19.
Pythagorean-hodograph (PH)曲线因其在弧长和等距线计算方面的优势而被广泛应用于曲线建模中.本文讨论了在总弧长约束下的三次PH曲线$G^2$连续拼接问题.具体地说,给定两个端点和一个拼接点,构造两条三次PH曲线,使其在指定总弧长下插值两个端点,并且在连接点处是$G^2$连续的.这也可以看作是一个曲线延拓问题.根据三次PH曲线的弧长公式和$G^2$连续条件,最终将问题转化为了一个带有约束的极小值问题,同时我们给出了几个具体例子来说明该方法. 相似文献
20.
Zaihong Wang 《Proceedings of the American Mathematical Society》1998,126(8):2267-2276
In this paper, we prove an infinity of periodic solutions to the periodically forced nonlinear Duffing equation .