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991.
Zheng-qiu Zhang Xian-wu Zeng Zhi-cheng WangCollege of Mathematics Wuhan University Wuhan . China College of Mathematics. Hunan University Changsha China 《应用数学学报(英文版)》2003,19(4):691-702
Abstract By using the continuation theorem of coincidence degree theory,the existence of a positive periodicsolution for a nonautonomous diffusive food chain system of three species. dx_1(t)/dt=x_1(t)[r_1(t)-a_(11)(t)x_1(t)-a_(12)(t)x_2(t)]+D_1(t)[y(t)-x_1(t)], dx_2(t)/dt=x_2(t)[-r_2(t)+a_(21)(t)x_1(t-r_1)-a_(22)(t)x_2(t)-a_(23)(t)x_3(t)], dx_3(t)/dt=x_3(t)[-r_3(t)+a_(32)(t)x_2(t-r_2)-a_(33)(t)x_3(t)], dy(t)/dt=y(t)[r_4(t)-a_(44)(t)y(t)]+D_2(t)[x_1(t)-y(t)]+D_2(t)[x_1(t)-y(t)],is established,where,r_i(t),a_(ii)(t)(i=1,2,3,4),D_i(t)(i=1,2),a_(12)(t),a_(21)(t),a_(23)(t)and a_(32)(t) are all positiveperiodic continuous functions with period w>0,T_i(i=1,2)are positive constants. 相似文献
992.
Given a closed convex set K in Rn; a vector function F:K×K Rm; a closed convex (not necessarily pointed) cone P(x) in m with non-empty interior, PP(x) Ø, various existence results to the problemfind xK such that F(x,y)- int P(x) y K
under P(x)-convexity/lower semicontinuity of F(x,) and pseudomonotonicity on F, are established. Moreover, under a stronger pseudomonotonicity assumption on F (which reduces to the previous one in case m=1), some characterizations of the non-emptiness of the solution set are given. Also, several alternative necessary and/or sufficient conditions for the solution set to be non-empty and compact are presented. However, the solution set fails to be convex in general. A sufficient condition to the solution set to be a singleton is also stated. The classical case P(x)=m
+ is specially discussed by assuming semi-strict quasiconvexity. The results are then applied to vector variational inequalities and minimization problems. Our approach is based upon the computing of certain cones containing particular recession directions of K and F. 相似文献
993.
Petra Sindelá rová 《Proceedings of the American Mathematical Society》2003,131(7):2089-2096
We show that there is a continuous map of the unit interval into itself of type which has a trajectory disjoint from the set of recurrent points of , but contained in the closure of . In particular, is not closed. A function of type , with nonclosed set of recurrent points, was found by H. Chu and J. Xiong [Proc. Amer. Math. Soc. 97 (1986), 361-366]. However, there is no trajectory contained in , since any point in is eventually mapped into . Moreover, our construction is simpler.
We use to show that there is a continuous map of the interval of type for which the set of recurrent points is not an set. This example disproves a conjecture of A. N. Sharkovsky et al., from 1989. We also provide another application of .
994.
Philippe Cieutat 《Journal of Differential Equations》2003,190(1):108-130
We study some properties of bounded and almost periodic solutions of convex Lagrangian systems in the presence of almost periodic forcing
995.
Yang Haitao 《Journal of Differential Equations》2003,189(2):487-512
The following singular elliptic boundary value problem is studied:
996.
王在洪 《数学年刊A辑(中文版)》2003,(1)
本文研究二阶微分方程χ"+aχ+-bχ-+f(χ)g(χ'=p(t)周期解的存在性,这里χ+=max{χ,0},χ-=max{-χ,0},a,6是正常数并且点(a,b)位于某一条Fucik谱曲线上.当g(χ)的极限lim.g(χ)=g(+∞),lim g(χ)=g(-∞)和f(χ)的极限lim,g(χ)=f(+∞),lim f(χ)=f(-∞)都存在且有限时,给出了此方程存在周期解的充分条件. 相似文献
997.
In this paper, we establish existence results for positive solutions for the (n−1,1) three-point boundary value problems consisting of the equation
998.
We study the class of bounded C
0-semigroups T=(T
t
)
t0 on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X
0(T)<, where X
0(T):={x X:limt T
t
x=0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality. 相似文献
999.
1000.
K. L. Boey Patricia J. Y. Wong Y. C. Soh 《Nonlinear Analysis: Real World Applications》2003,4(5):787-804
The modelling of the spread of infectious disease is carried out for time t on a measure chain T. Our approach unifies the continuous case
and the discrete case
. The model is described by the integral equationwhere x(t) represents the proportion of the population infected at time t, f(t,x(t)) denotes the proportion of the population newly infected per unit time, and τ is the length of time an individual remains infectious. Using the measure chain calculus, we shall develop criteria for the existence of a nontrivial and nonnegative periodic solution for the modelling equation. The criteria can be implemented numerically, for this we shall give an algorithm as well as illustrative examples. 相似文献