共查询到20条相似文献,搜索用时 140 毫秒
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
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.
步起跃 《数学年刊A辑(中文版)》2000,(4)
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.
4.
颜跃新 《高校应用数学学报(A辑)》1999,14(2):135-139
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.
赵兴球 《数学年刊A辑(中文版)》1995,(3)
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.
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 .
If , then the set in the above inequality can be replaced by .
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.
A. V. Demyanov 《Journal of Mathematical Sciences》2006,136(2):3706-3717
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.
V. N. Denisov 《Journal of Mathematical Sciences》2008,150(5):2344-2357
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.
Bai Zhanbing Liang Xiangqian Li Weiming 《高校应用数学学报(英文版)》2007,22(1):13-20
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.
Donatella Donatelli Pierangelo Marcati 《Transactions of the American Mathematical Society》2004,356(5):2093-2121
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:
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.