一类新型时滞积分不等式及其应用

主要研究了一种新型时滞积分不等式u(t)≤a(t)+∫0α(t)f(t,s)w(u(s))ds+∫0α(t)g(t,s∫)0sh(s,τ)φ(u(τ))dτds up(t)≤a(t)+p/p-q∫0α(t)(f(t,s)uq(s)w(u(s))+g(t,s)uq(s))dsup(t)≤a(t)+p/p-q∫0α(t)f(t,s)uq(s)w(u(s))ds+p/p-q∫0tg(t,s)uq(s)w(u(s))ds这里p>q≥0是常数且t∈[0,∞).并且用此结果研究了时滞微分积分方程解的全局存在性和有界性.     

具有无限时滞的二阶微分方程解的存在性

§ 1.　IntroductionRecently ,thedifferentialequationswithdeviatingargumentswereusuallydiscussed(see[1 ],[4],[5 ]) .In [1 ],AGARWALRPandO’REGANDconsideredequationy″(t) =f(t,y(t) ,y(σ(t) ) ) ,　a.e .t∈ [0 ,1 ]y(t) =ψ(t) ,　　　　　　　　t∈ [-r ,0 ]y( 1 ) =a ,( )andtheydiscussedtheexistenceofatleastonesolutionforequation ( ) .Inthispaper ,weconsideramoregeneralequation-x″(t) =f(t ,xt) ,　t∈ [0 ,1 ]x(t) =ψ(t) ,　　　　t∈ ( -∞ ,0 ]x( 0 ) =x( 1 ) =0 ,( 1 .1 )andsomeexistencetheor…     

Some oscillation criteria for second order nonlinear functional ordinary differential equations

The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations (a(t)x'(t))' δ1p(t)x'(t) δ2q(t)f(x(g(t))) = 0,for 0 ≤ t0 ≤ t, where δ1 = ±1 and δ2 = ±1. The functions p,q,g : [t0, ∞) → R, f :R → R are continuous, a(t) ＞ 0, p(t) ≥ 0,q(t) ≥ 0 for t ≥ t0, limt→∞ g(t) = ∞, and q is not identically zero on any subinterval of [t0, ∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable.     

具连续变量脉冲差分方程解的振动性

考虑新的一类具有连续变量的脉冲差分方程x(t τ) - x(t) p(t)x(t - rτ) =0,x(tk τ) - x(tk) = bkx(tk),　t≥t0 -τ,t≠tk,t∈N(1),其中p(t)是[t0 -τ,∞]上的非负连续函数,τ>0,bk 是常数,r是正整数, 0≤t0 < t1 < t2 <…< tk <…且limk→∞tk =∞,获得了方程所有解振动的充分条件.     

Preconditioned Conjugate Gradient Methods for Integral Equations of the Second Kind Defined on the Half-Line

1.IntroductionInthispaPer,westudynumericalsolutionstointegralequationsofthesecondkinddefinedonthehalfline.Morepreciselyweconsidertheequationy(t)+Iooa(t,s)y(s)ds=g(t),OS相似文献   

一阶时滞泛函微分方程解的零点距估计

研究时滞微分方程x′(t) p(t) x(t-τ) =0 ,t≥ t0 , (1)(x(t) a(t) x(t-δ) )′ b(t) x(t-σ) =0 ,t≥ t0 ,(2 )的解的零点距 .采用一种新方法 ,给出其解任意两相邻零点之间的距离的估计 ,改进、推广已有的结果     

一类二阶非线性泛函微分方程的振动性

本文讨论二阶非线性泛函微分方程(a(t)y′(t))′+p(t)y′(t-τ(t))-q(t)f(y(t))=0,t≥t₀,(1)(a(t)y′(t))′-p(t)y′(t+τ(t))-q(t)f(y(t))=0,t≥t₀,(2)获得了方程(1)和(2)振动的充分性判据,推广和改进了已知的一些结果.     

FINITE ELEMENT ANALYSIS OF A LOCAL EXPONENTIALLY FITTED SCHEME FOR TIME-DEPENDENTCONVECTION-DIFFUSION PROBLEMS

1.IntroductionConsiderthetime-dependentconvection-diffusionproblemat--Euzx a(x,t)u. b(x,t)u~f(x,t),(x,t)E[0,1]x[0,T](1.1)u(0,t)=u(1,t)~0,tE[0,T].(1.2)u(x,0)=u000,xE[0,1],(1.3)a(x,t)2or>0,(1.4)b(x,t)--a.(x,t)/220>0,(1.5)where0SE<<1'(1.1)-(1.5)canbereg...     

变系数Euler-Bernoulli梁振动发展系统的存在性

讨论变系数Euler-Bernoulli梁振动系统{uu(x,t) η(t)uxxxx(x,t)=0,0＜x＜1,0≤t≤T u(0,t)=ux(0,t)=0,0≤t≤t -uxxx(1,t) muu(1,t)=-αu1(1,t) βuxxx(1,t),0≤t≤T uxt(1,t) =-γuxx(1,t),0≤t≤t u(x,0)=u1(x),u1(x,0),0≤x≤1证明了该系统产生一个发展系统．     

二阶中立型线性微分差分方程的非振动解的类型与判别

本文考虑二阶中立型线性微分差分方程x″(t)-cx″(t-r) px[g(t)]=0.x″(t)-cx″(t-r) p(t)x[g(t)]=0.其中 r>0,p>0,p(t)>0,1>c≥0,g(t)≤t,g(t)= ∞.给出了仅有的几种满足x(t)[x(t)-cx(t-r)]>0的非振动解的类型且得到了一些判别的充分条件.     

ASYMPTOTIC STABILITY FOR A CLASS OF NONAUTONOMOUS NEUTRAL DIFFERENTIAL EQUATIONS

ＡＳＹＭＰＴＯＴＩＣＳＴＡＢＩＬＩＴＹＦＯＲＡＣＬＡＳＳＯＦＮＯＮＡＵＴＯＮＯＭＯＵＳＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ＊＊ＹＵＪＩＡＮＳＨＥ＊ＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕｌｙ４，１９９５．ＲｅｖｉｓｅｄＭａｒｃｈ２...     

关于一个二阶非线性中立时滞微分方程的非振荡解的存在性

A new second-order nonlinear neutral delay differential equation r（t） x（t） ＋ P（t）x（t-τ） ＋ cr（t） x（t）-x（t-τ） ＋ F t,x（t-σ1）,x（t-σ2）,...,x（t-σn） = G（t）,t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ 0,P,r ∈ C（[t0,＋∞）,R）,F ∈ C（[t0,＋∞）×Rn,R）,G ∈ C（[t0,＋∞）,R） and c is a constant,is studied in this paper,and some sufficient conditions for existence of nonoscillatory solutions for this equation are established and expatiated through five theorems according to the range of value of function P（t）.Two examples are presented to illustrate that our works are proper generalizations of the other corresponding results.Furthermore,our results omit the restriction of Q1（t） dominating Q2（t）（See condition C in the text）.     

带参数的一阶泛函差分方程的定号周期解

In this paper,the authors obtain the existence of one-signed periodic solutions of the first-order functional difference equation ?u(n) = a(n)u(n)-λb(n)f(u(n-τ(n))),n ∈ Z by using global bifurcation techniques,where a,b:Z → [0,∞) are T-periodic functions with ∑T n=1 a(n) 0,∑T n=1 b(n) 0;τ:Z → Z is T-periodic function,λ 0 is a parameter;f ∈ C(R,R) and there exist two constants s_2 0 s_1 such that f(s_2) = f(0) = f(s_1) = 0,f(s) 0 for s ∈(0,s_1) ∪(s_1,∞),and f(s) 0 for s ∈(-∞,s_2) ∪(s_2,0).     

二阶两点边值问题单调正解的存在性

考察了形如{x″(t)+f(t,x(t))=0,0≤t≤1,x(0)=ξx(1),x′(1)=ηx′(0)的二阶非线性微分方程两点边值问题,这里ξ,η∈(0,1)∪(1,∞)为给定的常数,f:[0,1]×[0,∞)→[0,∞)连续。在某些适当的增长性条件下,应用Avery-Anderson-Krueger不动点定理证明了单调正解的存在性。     

带一类时滞项的生物种群扩散模型的行波解

本文利用Schauder不动点理论证明了微分积分方程组行波解u（x，t）＝U（z）,w（x,t）＝W（z）,z＝xγ－ct的存在性．这个方程组描述了一类在植物上繁殖，且靠飞行在空中扩散的生物种群扩散过程．特别当时滞项，中积分核K（t）（反映种群繁殖模式）属于L1（0，∞）时，本文得到极限值W（－∞）（表示最终植物上种群密度）小于M．这个结论较符合生物实际．     

二阶三点边值问题的正解

该文讨论了二阶三点边值问题$-u'(t)=b(t)f(u(t))$满足$u'(0)=0$, $u(1)={\alpha}u({\eta})$ 正解的存在性与多重性, 其中常数$\alpha, \eta\in(0,1)$, $f\in C ([0,\infty),[0,\infty) )$, $b\in C ([0,1],[0,\infty) )$且存在$t_0\in[0,1]$使$b(t_0)>0$. 利用该问题相应的Green函数, 将其转化为Hammerstein型积分方程, 借助于锥上的不动点指数理论,给出了该问题单个正解和多个正解存在的与其相应线性问题的第一特征值有关的最佳充分性条件.     

半拟线性p-Laplacian问题结点解的存在性

In this paper, we study the existence of nodal solutions for the following problem:-(φ_p(x′))′= α(t)φ_p(x~+) + β(t)φ_p(x~-) + ra(t)f(x), 0 t 1,x(0) = x(1) = 0,where φ_p(s) = |s|~(p-2)s, a ∈ C([0, 1],(0, ∞)), x~+= max{x, 0}, x~-=- min{x, 0}, α(t), β(t) ∈C[0, 1]; f ∈ C(R, R), sf(s) 0 for s ≠ 0, and f_0, f_∞∈(0, ∞), where f_0 = lim_|s|→0f(s)/φ_p(s), f_∞ = lim|s|→+∞f(s)/φ_p(s).We use bifurcation techniques and the approximation of connected components to prove our main results.     

二阶线性中立时滞方程非振动解的存在性

考虑具有正负系数的中立时滞微分方程这里P∈R和τ∈(0,∞),σ1,σ2∈[0,∞)且Q1,Q2∈C([t0,∞),R+).对于上面方程非振动解的存在性,得到一个用,∫sQids <∞,i=1,2,来表达的充分条件。这个结果去掉了M.R.S.Kulenovic和S.Hadziomerspahic文中一个相当强的假设,改进了其中的相关定理.     

多维非退化扩散过程的象集与图集的一致Packing维数

设B(t)=(B(t))=(B1(t),B2(t),…,BN(t))为N维Brown运动,设α(x)=(αij(x),1(≤)I(≤)d,1(≤)j(≤)N),β(x)=(βi(x),1(≤)I(≤)d),x∈Rd,1(≤)d(≤)N,α(x)和β(x)有界连续和满足Lipchitz条件,且存在常数c0＞0,使得对每个x∈Rd,a(x)=α(x)α(x)*的每个特征根都不小于c0.设dX(t)=α(X(t))dB(t) β(X(t))dt,设d(≥)3.可以证明P(ωDimX(E,ω)=DimGRX(E,ω)=2DimE,(A)E∈B[0,∞))=1.这里X(E,ω)={X(t,ω)t∈E},GRX(E,ω)={(t,X(t,ω))t∈E},DimF表示F的Packing维数.     

Refined asymptotic profiles for a semilinear heat equation

We study the large time behavior of the solutions of the Cauchy problem for a semilinear heat equation,