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1.
关于偶数阶中立型微分方程的线性化振动的一个注记   总被引:2,自引:0,他引:2  
李永昆  徐贵桐 《数学学报》2000,43(3):531-534
就偶数阶中立型时滞微分方程的所有有界解的振动性而言,研究了偶数阶非 线性中立型时滞微分方程[x(t)-p(t)x(t-τ)]-q(t)h(x(t-σ))=0和与它相应的 线性方程[x(t)-p_0x(t-τ)]-q-0x(t-τ)=0在振动性上的等价性.所得结果改进 了 Ladas G,和 Qian C.的一个结果.  相似文献   

2.
本文研究非线性薛定鄂方程的初始值和边界值问题 iu_t=u_(xx)-g|u|~(p-1)u。0<x,t<∞,这里 g> 0, p> 3; u(x,0)= h(x).假设 h(x)∈ H(IR~+), Q(t),R(t) E C(IR~+).对于二类不同的边界值(狄里克莱型u(0,t)=Q(t)和鲁宾型u_x(0,t)+au(0,t)=R(t);这里a是实数)本文证明古典解。 u∈ C~1(L~2)∩ L~2(H~2)的存在性,唯一性和全局性.  相似文献   

3.
一、填空题1.某数的12比它的3倍小4,则这个数为.2.当x=时,代数式x-1与2x-14相等.3.单项式3a2+xb4与-12a5b2(y-3)是同类项,则x=,y=.4.在公式S=12(a+b)h中,S=120,h=15且b=2a,则a=.5.填出解方程0.1-0.2x0.3=1-0.01x-0.020.06各步的依据:解 1-2x3=1-x-26(  )2(1-2x)=6-(x-2)(  )2-4x=6-x+2(  )-4x+x=6+2-2(  )-3x=6(  )x=-2(  )6.三个…  相似文献   

4.
本文主要研究了强迫振动方程:x+(f(x)+g(x)x)X+h(x)=e(t)的解的有界性以及周期解的存在性,这里f(x),g(x),h(x)在(-∞,+∞)中连续,e(t)在「0,+∞)上连续,得到了解的有界性与存在周期解的条件。  相似文献   

5.
Inthispaper,wehaveobtainedthefollowingtheorems.Theorem1 Letφ(x)beaincreasingfunctionon[0,+∞),φ(x)→+∞andφ(x)xbeno-increasing(Whenxislargeenough),andletBbeaseparableBanachspace,XbeaB-valuedrandomvariable,ifi)X∈WM20ii)Xτ-EXτ∈CLT,τ>0,whereXτ=XI{yXy≤τ}ii…  相似文献   

6.
最佳L2局部逼近存在唯一的充分必要条件   总被引:1,自引:0,他引:1  
本文给出了最佳L2局部逼近的存在唯一性定理,设f∈L2(0,δ),Sn=span(u0,u1,...Un-1)C^n-1(0,δ),且detWn(u0,u1,...un-1;0)≠0,那么,当x→0时,网(Px(f,Sn)收敛于Sn中某元素P0(f,Sn)的充要条件为:f=Pn-1+h,其中Pn-1(t)=n-1∑i=1aiti(h,1)x=0(X^n),x→0,且P0(f,Sn)=UW^-1nA  相似文献   

7.
1.引言考虑奇阶非线性泛函微分方程[x(t)-cx(t—()](n)+p(t)f(x(t-σ))=0(1)对方程(1)我们作如下假设(H):(H1)n>1是奇整数,p∈C((t0,∞),(t0,∞));(H2)τ>0,σ>0且0≤c≤1;(H3)f∈C(R,R)是单调增加,xf(x)>0,X≠0且当|x|→∞时有|f(t)|→∞.设δ=max{τ,σ},∈C([T-δ,T],R).方程(1)在[T,∞)上的解是指函数x∈C([T,∞),R),使得x(t)=((t),T-δ≤t≤T,[x(t)-cx…  相似文献   

8.
设(Xi,Yi)1≤i≤n为来自二元总体(X,Y)的平稳,φ-混合样本,记m(x)△E(Y│X=x),m(x)的一种递推型核估计为mn(x)=n∑i=1hi^-1Yik((x-Xi)/hi)/n∑j=1h^-1jk(x-Xj)/hj)。本文在一定的条件下证明了(n/(n∑j=1h^-1j)^1/2)(mn(x1)-m(x1),mn(x2)-m(x2),...mn(xr0)-m(xr0))′依分布收  相似文献   

9.
本文考虑R~d中具有如下形式的过程:X(t)=(X_1(t),X_2(t),…,X_N(t)),其中X_i(t)为R~di中指标为α_i的稳定过程(1≤i≤N),X_1(t),…,X_N(t)相互独立,d=d1+…+d_N.通过讨论过程G(t)=(t,X(t))的逗留时分布的渐近性质,研究图集G[0,1]的Packing测度函数问题。获得了ψ-p(G[0,1])=0或+∞的积分判别法,或者其确切测度函数.  相似文献   

10.
指数有界C-半群的共轭半群   总被引:7,自引:0,他引:7  
令S(t)是Banach空间X上的指数有界C-半群,S(t)是它在共轭空间X上的共轭半群.本文给出了X的一个闭子空间X+,使得S(t)在X+上的限制S+(t)是C|x+-半群,并给出了S+(t)的生成元.空间X+在某种意义上有极大性.  相似文献   

11.
定义F={t>0,F(t)=1},设t<τ  相似文献   

12.
We prove the following extended version of Simons' inequality and present its applications. Let be a set and be a subset of . Let be a subset of a Hausdorff topological vector space which is invariant under infinite convex combinations. Let be a bounded function such that the functions are convex for all and whenever 0$">, and Let be a sequence in . Assume that, for every , there exists satisfying . Then


If , then the set in the above inequality can be replaced by .

  相似文献   


13.
具强迫力的奇数阶中立型微分方程的振动性   总被引:3,自引:0,他引:3  
Abstract. In this paper, the forced odd order neutral differential equations of the form are con-sidered  相似文献   

14.
The problem of establishing necessary and sufficient conditions for l.s.c. under PDE constraints is studied for a special class of functionals:
with respect to the convergence un → u in measure, vn ⇀ v in Lp(Ω;ℝd) in W−1,p(Ω), and χn ⇀ χ in Lp(Ω), where χn ∈ Z:= {χ ∈ L(Ω): 0 ≤ χ(x) ≤ 1 for a.e. x}. Here is a constant-rank partial differential operator. The main result is that if the characteristic cone of has the full dimension, then the l.s.c. is equivalent to the fact that the F± are both -quasiconvex and
for a.e. x ∈ Ω and for all u ∈ ℝd. As a corollary, we obtain several results for the functional
with respect to the same convergence. We show that this functional is l.s.c. iff
Bibliography: 14 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 100–119.  相似文献   

15.
In the paper, we study the sufficient conditions for the lower-order coefficient of the parabolic equation
under which its solution satisfying the initial condition
stabilizes to zero, i.e., there exists the limit
uniform in x from every compact set K in ℝN for any function u 0(x) belonging to a certain uniqueness class of the problem considered and growing not rapidly than with a > 0 and b < 0 at infinity. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 79–97, 2006.  相似文献   

16.
该文研究一类时滞微分方程边值问题〖JB({〗εx″(t)=f(t,x(t),x(t-τ(t)),\[Tx\](t),x′(t),ε),t∈(0,1),\=x(t)=φ(t,ε),t∈\[-τ,0\],h(x(1),x′(1),ε)=A(ε),[JB)]其中ε>0为小参数,τ(t)≥τ\-0>0,τ=\%\{max\}\%[DD(X]t∈\[0,1\][DD)]τ(t)<1,\[Tx\](t)=ψ(t)+∫\+t\-0k(t,x)x(s)ds为Volterra型算子。利用微分不等式理论证明了边值问题解的存在性,并给出了解的一 致有效渐近展开式。  相似文献   

17.
中立型二阶非线性微分方程振动性的判据   总被引:7,自引:0,他引:7  
Abstract. In this paper ,the oscillation criteria for the solutions of the nonlinear differential e-quations of neutral type of the forms:  相似文献   

18.
In this paper, we discuss the conditions for a center for the generalized Liénard system (E)1
or (E)1
with f(x), g(x),(y),\ (y),\ h(y)\colon , F(x) = 0x f(x)dx, and xg(x) > 0 for x 0. By using a different technique, that is, by introducing auxiliary systems and using the differential inquality theorem, we are able to generalize and improve some results in [1], [2].  相似文献   

19.
This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type(φ(x'(t)))' q(t)f(t,x(t),x'(t)) = 0, t ∈ (0, 1),subject to the following boundary condition:a1φ(x(0)) - a2φ(x'(0)) = 0, a3φ(x(1)) a4φ(x'(1)) = 0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem,sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.  相似文献   

20.
In this paper we investigate the diffusive zero-relaxation limit of the following multi-D semilinear hyperbolic system in pseudodifferential form:


We analyze the singular convergence, as , in the case which leads to a limit system of parabolic type. The analysis is carried out by using the following steps:
(i)
We single out algebraic ``structure conditions' on the full system, motivated by formal asymptotics, by some examples of discrete velocity models in kinetic theories.
(ii)
We deduce ``energy estimates ', uniformly in , by assuming the existence of a symmetrizer having the so-called block structure and by assuming ``dissipativity conditions' on .
(iii)
We assume a Kawashima type condition and perform the convergence analysis by using generalizations of compensated compactness due to Tartar and Gérard.
Finally, we include examples that show how to use our theory to approximate any quasilinear parabolic systems, satisfying the Petrowski parabolicity condition, or general reaction diffusion systems, including Chemotaxis and Brusselator type systems.

  相似文献   


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