首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到19条相似文献,搜索用时 156 毫秒
1.
张建平  蔡果兰 《数学季刊》2006,21(3):375-380
Consider the following equations: Where 0 <η< 1,0 <α< 1, and f : [0,1]×[0,∞)→[0,∞), Ii,Li : [0,∞)→R, (i = 1,2,…, k) are continuous functions. We prove the existence of eigenvalues for the problem under a weaker condition, moreover we do not require the monotonicity of the impulsive functions.  相似文献   

2.
Periodicity in a Nonlinear Predator-prey System with State Dependent Delays   总被引:1,自引:0,他引:1  
With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following nonlinear state dependent delays predator-prey system where a_i(t),c_j(t),d_i(t) are continuous positive periodic functions with periodic ω>0, b_1(t),b_2(t) are continuous periodic functions with periodic ωand ∫_0~ωbi(t)dt>0. T_i,σ_j, p_i (i=1,2,…,n, j=1, 2,…,m) are continuous and ω-periodic with respect to their first arguments, respectively, α_i, β_j,γ_i(i=1,2,…,n, j=1,2, …, m) are positive constants.  相似文献   

3.
With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a differential-integral predator-prey system with infinite delaywhere N1(t), N2(t) satisfy N1(t) =φ1(t), N2(t) =φ2(t), φi∈ BC((∞,0],R+φi(0)> 0,i=1,2, ∫0+∞Ki(s)ds = 1, i=1,2,3.  相似文献   

4.
This article is concerned with the oscillation of the forced second order differential equation with mixed nonlinearities a(t) x ′ (t) γ′ + p 0 (t) x γ (g 0 (t)) + n i =1 p i (t) | x (g i (t)) | α i sgn x (g i (t)) = e(t), where γ is a quotient of odd positive integers, α i > 0, i = 1, 2, ··· , n, a, e, and p i ∈ C ([0, ∞ ) , R), a (t) > 0, gi : R → R are positive continuous functions on R with lim t →∞ g i (t) = ∞ , i = 0, 1, ··· , n. Our results generalize and improve the results in a recent article by Sun and Wong [29].  相似文献   

5.
In this paper,we are interested in the existence of positive solutions for the Kirchhoff type problems{-(a_1 + b_1M_1(∫_?|▽u|~pdx))△_(_pu) = λf(u,v),in ?,-(a_2 + b_2M_2(∫?|▽v|~qdx))△_(_qv) = λg(u,v),in ?,u = v = 0,on ??,where 1 p,q N,M i:R_0~+→ R~+(i = 1,2) are continuous and increasing functions.λ is a parameter,f,g ∈ C~1((0,∞) ×(0,∞)) × C([0,∞) × [0,∞)) are monotone functions such that f_s,f_t,g_s,g_t ≥ 0,and f(0,0) 0,g(0,0) 0(semipositone).Our proof is based on the sub-and super-solutions techniques.  相似文献   

6.
We consider the nonautonomous cooperative system with continuous time delay (x)(t)=x(t)[a1(t)-a2(t)+a3(t)∫o-Tk1(s)x(t+s)ds-a4(t) ∫o-Tk2(s)y(t+s)ds] (y)(t)=y(t)[b1(t)-b2(t)y(t)+a3(t) ∫o-Tk3(s)y(t+s)ds-b4(t) ∫o-Tk4(s)x(t+s)ds](1)where ai(t),bi(t)(i=1,2,3,4) are assumed to be continuous, positive and ω-periodic functions; and x(t),y(t) are the density of species; ki(s) (i=1,2,3,4) denote nonnegative piecewise continuous defined in [-τ,0] (there 0<τ<+∞) and normalized such that ∫o-T ki(s)ds=1. Let fL=inf{f(t):t∈R}, fM=sup{f(t),t∈R}, for a continuous and bounded function f(t).  相似文献   

7.
Locccal splmes are presented far the approximation of functions of one and many variables,which are ana-lytic in the domams where Ui(zi) is a unit disk in the complex plane Ci,i=1,2,...l,l=1,2,...Results arc given for functions whose r-order derivatives belong to the Hardy's class Hp,1≤p≤∞,It isshown that the approximation converge to the function at the rate Aexp(-Cn(r-1/p)for functions of one variable and An-(r-1/p)/(I-1) for functions of l variables,where n is the number of points of local splines and A and C are positrve constants.  相似文献   

8.
In this article, the author studies the boundedness and convergence for the {(x) = a(y) - f(x),(y) = b(y)β(x) - g(x) e(t),where a(y), b(y), f(x),g(x),β(x) are real continuous functions in y ∈ R or x ∈ R,β(x) ≥ 0 for all x and e(t) is a real continuous function on R = {t: t ≥ 0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended.  相似文献   

9.
Let {us(x) : s ≥ 0 , x ∈R} be a random string taking values in Rd . The main goal of this paper is to discuss the characteristics of the polar functions of {u s(x) : s ≥ 0 , x∈R} . The relationship between a class of continuous functions satisfying the H¨older condition and a class of polar-functions of {us (x) : s ≥ 0 , x ∈R} is presented. The Hausdorff and packing dimensions of the set that the string intersects a given non-polar continuous function are determined. The upper and lower bounds are obtained for the probability that the string intersects a given function in terms of respectively Hausdorff measure and capacity.  相似文献   

10.
The regularity of solutions to the Boltzmann equation is a fundamental problem in the kinetic theory. In this paper, the case with angular cut-off is investigated. It is shown that the macroscopic parts of solutions to the Boltzmann equation, i.e., the density, momentum and total energy are continuous functions of(x, t) in the region R3×(0, +∞). More precisely, these macroscopic quantities immediately become continuous in any positive time even though they are initially discontinuous and the discontinuities of solutions propagate only in the microscopic level. It should be noted that such kind of phenomenon can not happen for the compressible Navier-Stokes equations in which the initial discontinuities of the density never vanish in any finite time, see [22]. This hints that the Boltzmann equation has better regularity effect in the macroscopic level than compressible Navier-Stokes equations.  相似文献   

11.
We consider the multidimensional abstract linear integral equation of Volterra type x(t) (*)∫Rtα(s)x(s)ds=f(t),t∈R,(1)as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions. The functions x, α and f are Bauach space-valued defined on a compact interval R of R^n Rt is a subinterval of R depending on t ∈ R and (*) f denotes either the Bochner-Lebesgue integral or the Henstock integral. The results presented here generalize those in [1] and are in the spirit of [3]. As a consequence of our approach, it is possible to study the properties of (1) by transferring the properties of the discrete systems, The Henstock integral setting enables us to consider highly oscillating functions.  相似文献   

12.
§1 IntroductionAnvarovandLarinov[1]introducedthefollowingprey-predatorsystem:x(t)=x(t)[α-γy(t)-γ∫∞0K1(s)y(t-s)ds-∫∞0∫∞0R1(s,θ)y(t-s)y(t-θ)dθds],y(t)=y(t)[-β μx(t) μ∫∞0K2(s)x(t-s)ds ∫∞0∫∞0R2(s,θ)x(t-θ)x(t-s)dθds],(1)whereα,γ,βandμarepositiveconstants,Ki∈C([0,∞),(0,∞))andRi∈C([0,∞)×[0,∞),(0,∞)),i=1,2.Fortheecologicalsenseofsystem(1),wereferto[1,2]andrefer-encescitedtherein.Sincerealisticmodelsrequiretheinclusionoftheeffectofchangingen-vironment,itmot…  相似文献   

13.
14.
This paper is concerned with a nonlocal hyperbolic system as follows utt = △u + (∫Ωvdx )^p for x∈R^N,t〉0 ,utt = △u + (∫Ωvdx )^q for x∈R^N,t〉0 ,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈R^N,u(x,0)=u0(x),ut(x,0)=u01(x) for x∈R^N, where 1≤ N ≤3, p ≥1, q ≥ 1 and pq 〉 1. Here the initial values are compactly supported and Ω belong to R^N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed.  相似文献   

15.
Some results concerning existence of positive solutions for the singular boundary value problems u^(4)(t)=f(t,u(t)) t∈(0,1) u(0)=u(1)=0 u‘(0)=u‘(1)=0 have been given, where f(t, x) may be singular at t = 0, 1.  相似文献   

16.
SOME INTEGRAL INEQUALITIES FOR THE POLAR DERIVATIVE OF A POLYNOMIAL   总被引:1,自引:0,他引:1  
If P(z) is a polynomial of degree n which does not vanish in |z| 1,then it is recently proved by Rather [Jour.Ineq.Pure and Appl.Math.,9 (2008),Issue 4,Art.103] that for every γ 0 and every real or complex number α with |α|≥ 1,{∫02π |D α P(e iθ)| γ dθ}1/γ≤ n(|α| + 1)C γ{∫02π|P(eiθ)| γ dθ}1/γ,C γ ={1/2π∫0 2π|1+eiβ|γdβ}-1/γ,where D α P(z) denotes the polar derivative of P(z) with respect to α.In this paper we prove a result which not only provides a refinement of the above inequality but also gives a result of Aziz and Dawood [J.Approx.Theory,54 (1988),306-313] as a special case.  相似文献   

17.
In the present paper, we derive the Laplace transforms of the integral functionals
and
where p and q are real numbers, {B t (μ) : t ≥ 0} is a Brownian motion with drift μ > 0 (denoted BM(μ)), and {R t (3) : t ≥ 0} is a 3-dimensional Bessel process (denoted BES(3)). The transforms are given in terms of Gauss' hypergeometric functions, and the results are closely related to some results for functionals of Jacobi diffusions. This work generalizes and completes some results of Donati-Martin and Yor and Salminen and Yor. Bibliography: 18 titles. __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 51–78.  相似文献   

18.
In this paper, we obtain positive solution to the following multi-point singular boundary value problem with p-Laplacian operator,{( φp(u'))'+q(t)f(t,u,u')=0,0〈t〈1,u(0)=∑i=1^nαiu(ξi),u'(1)=∑i=1^nβiu'(ξi),whereφp(s)=|s|^p-2s,p≥2;ξi∈(0,1)(i=1,2,…,n),0≤αi,βi〈1(i=1,2,…n),0≤∑i=1^nαi,∑i=1^nβi〈1,and q(t) may be singular at t=0,1,f(t,u,u')may be singular at u'=0  相似文献   

19.
A group of necessary and sufficient conditions for the nonoscillation of a second order linear delayequation with impulses(r(t)u')'=-p(t)u(t-τ)are obtained in this paper,where p(t)=sum from ∞to n=1 a_n δ(t-t_n),δ(t) is a Dirac δ-unction,and for each n∈N,a_n>0,t_n→∞as n→∞.Furthermore,the boundedness of the solutions is also investigated if the equationis nonoscillatory.An example is given to illustrate the use of the main theorems.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号