POSITIVE PERIODIC SOLUTIONS OF FUNCTIONAL DISCRETE SYSTEMS AND POPULATION MODELS YOUSSEF N RAFFOUL doc

... A.DattaandJ.Henderson,Differences and smoothness of solutions for functional difference equa- tions, Proceedings of the First International Conference on Difference Equations (San An- tonio, Tex, ... Reid, and K. C. Yin, Positive solutions of nonlinear functional differ- ence equations,Comput.Math.Appl.42 (2001), no. 3-5, 639–646. [5] J.HendersonandW .N. Hudson,Eigenvalue prob...

Ngày tải lên: 23/06/2014, 00:20

... delay and Holling type III functional response. By us- ing the continuation theorem of coincidence degree theory and the method of Lyapunov functional, some sufficient conditions are obtained. 1. Introduction Many ... response functions (Holling [12]), Ivlev’s functional response (Ivlev [17]), and Rosenzweig functional response (Rosenzweig [22]). Systems with Holling-type fu...

Ngày tải lên: 23/06/2014, 00:20

... co- efficients on finite intervals. Moreover results obtained can be useful in investigation of such asymptotic problems as describing the asymptotic behavior of solutions and the investigation concerning ... formulas. Discrete systems of the form (1.1) containing only one delay are often called systems with pure delay. The main goal of the present paper is to extend the notion...

Ngày tải lên: 22/06/2014, 22:20

... as k →∞, and hence, u n+ n k → p ∗ n in C uniformly for n ∈ Z + as k →∞.Since u  n + n k +1  = F  n + n k ,u n+ n k  =  F  n + n k ,u n+ n k  − F  n + n k , p ∗ n  +  F  n + n k , p ∗ n  − G  n, ... j ∗ <ω. Now, set u k (n) = u (n + n k ). Notice that u n+ n k ( j) = u (n + n k + j) = u k (n + j) = u k n ( j )and hence, u n+ n k...

Ngày tải lên: 22/06/2014, 22:20

... that conditions 1 and 2 in Theorem 2.1 hold. Now we prove that the functional Φ satisfies PS condition on E. In the following, C denotes a universal positive constant, and ·, · denotes the ... of linear Hamiltonian systems with a nonlinear perturbation. Under generalized Ahmad-Lazer-Paul type coercive conditions for the nonlinearity on the kernel of the linear part, existen...

Ngày tải lên: 21/06/2014, 18:20

... t ∈ a n ,c n , and the function y n : u n − L/ρ 2 is strictly increasing on a n ,c n . We use ξ n to denote the inverse function of y n restricted to a n ,c n . In order to obtain 3.14, ... ∈ 0, 2π × 0, ∞1.2 and gu > 0 is nonincreasing and hu/gu is nondecreasing in u; G 3  there exist continuous, nonnegative functions g 1 u and h 1 u...

Ngày tải lên: 22/06/2014, 00:20

... Sh. Guseinov, “On the existence of positive solutions for nonlinear differ- ential equations with periodic boundary conditions,” Journal of Computational and Applied Mathematics, vol. 132, no. 2, ... Torres, and M. Zhang, Periodic solutions of second order non-autonomous singular dy- namical systems, ” Journal of Differential Equations, vol. 239, no. 1, pp. 196–212, 2007....

Ngày tải lên: 22/06/2014, 06:20

... Z × R n → R n is continuous in x ∈ R n for every n ∈ Z and is almost periodic in n ∈ Z uniformly for x ∈ R n , B : Z × Z × R n × R n → R n is continuous in x, y ∈ R n for any j ≤ n ∈ Z and is ... Y. Song and H. Tian, Periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay,” Journal of Computational and A...

Ngày tải lên: 22/06/2014, 11:20

... Ginzburg, and H. R. Akcakaya, Variations in plankton densities among lakes: A case for ratio-dependent models, Amer.Natural.138 (1991), 1287–1296. [3] R. Arditi, N. Perrin, and H. Saiah, Functional ... Functional responses and heterogeneities: An experimental test with cladocerans,OIKOS60 (1991), 69–75. [4] R. Arditi and H. Saiah, Empirical evidence of the role of heterogene...

Ngày tải lên: 23/06/2014, 00:20

... Zhong Nan Da Xue Qian Yan Yan Jiu Ji Hua under grant No. 2010QZZD015, Hunan Scientific Plan under grant No. 2011FJ6037, NSFC under grant No. 61070190 and NFSS under grant 10BJL020. References [1] ... that the environments of most natural populations change with time and that such changes induce variation in the growth characteristics of populations. Among many population models, th...

Ngày tải lên: 20/06/2014, 21:20