The main purpose of this paper is to discuss the existence and asymptotic behavior of solutions for [GRAPHICS] and for which the sufficient conditions of asymptotic behavior are obtained and the restriction for the ex...The main purpose of this paper is to discuss the existence and asymptotic behavior of solutions for [GRAPHICS] and for which the sufficient conditions of asymptotic behavior are obtained and the restriction for the existence is reduced.展开更多
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solution...Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.展开更多
In this paper, we investigate the following partial differential equation, ut , where a > 0 and p> 1. When n(p-1)/2 > 1 andp > 3, we obtained a nontrivial non-negative global solution. Furthermore, on Sobo...In this paper, we investigate the following partial differential equation, ut , where a > 0 and p> 1. When n(p-1)/2 > 1 andp > 3, we obtained a nontrivial non-negative global solution. Furthermore, on Sobolev space W1,s(W2,s) with s > 1. a nonuniqueness result is established which shows that there exists a positive solution u(t,x) with u(t,x)→0 as t→0 in W1,s(W2,s). On the other hand, our result can be regarded as a generalization of conclusion of Haraux, A.and Weissler, F.B. in [5].展开更多
In this paper, we consider the neutral difference equation△(x n-cx n-m )+p nx n-k =0, n=N, N+1, N+2, …,where c and p n are real numbers, k, m are positive integers with m<k, and △ den...In this paper, we consider the neutral difference equation△(x n-cx n-m )+p nx n-k =0, n=N, N+1, N+2, …,where c and p n are real numbers, k, m are positive integers with m<k, and △ denotes the forward difference operator: △ u n=u n+1 -u n. By using the Krasnoselskii fixed theorem, we obtain some sufficient conditions under which such an equation has a bounded and eventually positive solution which tends to zero as n→∞.展开更多
Generalized balanced tournament designs(GBTDs) are an equivalent characterization of a class of equitable symbol weight codes. Motivated by the construction of GBTDs, we establish in this paper an asymptotic existence...Generalized balanced tournament designs(GBTDs) are an equivalent characterization of a class of equitable symbol weight codes. Motivated by the construction of GBTDs, we establish in this paper an asymptotic existence theorem for frame-GBTDs of type gnand block size k via decompositions of edge-colored complete digraphs into prescribed edge-colored subgraphs.展开更多
In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--lo...In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--losing point. However,according to many practical experts, it is rather difficult to put such a phaselooked loop into practice, though it has fine properties. W. C. Lindsey [3] made a展开更多
In this paper we consider the initial boundary value problem for a class of reaction-diffusion system with time delay in population dynamics. We prove the existence and uniqueness of bounded nonnegative solution for ...In this paper we consider the initial boundary value problem for a class of reaction-diffusion system with time delay in population dynamics. We prove the existence and uniqueness of bounded nonnegative solution for the initial boundary value problem and discuss the asymptotic behaviour of the solution.展开更多
文摘The main purpose of this paper is to discuss the existence and asymptotic behavior of solutions for [GRAPHICS] and for which the sufficient conditions of asymptotic behavior are obtained and the restriction for the existence is reduced.
文摘Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
文摘In this paper, we investigate the following partial differential equation, ut , where a > 0 and p> 1. When n(p-1)/2 > 1 andp > 3, we obtained a nontrivial non-negative global solution. Furthermore, on Sobolev space W1,s(W2,s) with s > 1. a nonuniqueness result is established which shows that there exists a positive solution u(t,x) with u(t,x)→0 as t→0 in W1,s(W2,s). On the other hand, our result can be regarded as a generalization of conclusion of Haraux, A.and Weissler, F.B. in [5].
文摘In this paper, we consider the neutral difference equation△(x n-cx n-m )+p nx n-k =0, n=N, N+1, N+2, …,where c and p n are real numbers, k, m are positive integers with m<k, and △ denotes the forward difference operator: △ u n=u n+1 -u n. By using the Krasnoselskii fixed theorem, we obtain some sufficient conditions under which such an equation has a bounded and eventually positive solution which tends to zero as n→∞.
基金supported by National Natural Science Foundation of China(Grant Nos.11271280 and 11201328)Graduate Student Research and Innovation Program of Jiangsu Province(Grant No.CXZZ13 0794)
文摘Generalized balanced tournament designs(GBTDs) are an equivalent characterization of a class of equitable symbol weight codes. Motivated by the construction of GBTDs, we establish in this paper an asymptotic existence theorem for frame-GBTDs of type gnand block size k via decompositions of edge-colored complete digraphs into prescribed edge-colored subgraphs.
文摘In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--losing point. However,according to many practical experts, it is rather difficult to put such a phaselooked loop into practice, though it has fine properties. W. C. Lindsey [3] made a
文摘In this paper we consider the initial boundary value problem for a class of reaction-diffusion system with time delay in population dynamics. We prove the existence and uniqueness of bounded nonnegative solution for the initial boundary value problem and discuss the asymptotic behaviour of the solution.
