共查询到20条相似文献,搜索用时 109 毫秒
1.
具$p$-Laplacian 算子的多点边值问题迭代解的存在性 总被引:1,自引:0,他引:1
利用单调迭代技巧和推广的Mawhin定理得到下述带有p-Laplacian算子的多点边值问题迭代解的存在性,{(Фp(u'))' f(t,u, Tu)=0, 0(≤)t(≤)1,u(0)=q-1∑i=1γiu(δi),u(1)=m-1∑i=1ηiu(ξi),其中Фp(s)=|s|p-2s,p>1;0<δi<1,γi>0,1(≤)i(≤)q-1;0<ξi<1,ηi(≥)0,1(≤)i(≤)m-1且q-1∑i=1γi<1,m-1∑i=1ηi(≤)1;Tu(t)=∫t0k(t,s)u(s)ds,k(t,s)∈C(I×I,R ). 相似文献
2.
方程w"-w+f(t,w)=O的Dirichlet边值问题的正解存在性与多解性 总被引:1,自引:0,他引:1
姚庆六 《应用泛函分析学报》2002,4(1):4-9
考察了下列常微分方程的Dirichlet边值问题的正解[w″(t)-w(t) f(t,w(t))=0,0≤t≤1 w(0)=w(1)=0建立了n正解的存在性,其中n是一个任意的自然数。 相似文献
3.
该文研究了p-Laplacian 动力边值问题 (g(u△(t)))▽+a(t)f(t, u(t))=0, t ∈ [0, T] T, u(0)=u(T)=w, u△(0)=-u△(T) 正解的存在性. 其中w是非负实数, g(ν)=|ν| p-2ν, p>1 . 根据对称技巧和五泛函不动点定理, 证明了边值问题至少有三个正的对称解, 同时, 给出了一个例子验证了我们的结果. 相似文献
4.
5.
An iterative process of positive solution for BVP w"+h(t)f(w)=0,w(0)=w(1)-0 is established, where h(t) is allowed to changes sign on [0,1]. The process starts from a simple function. 相似文献
6.
三阶奇异边值问题的正解 总被引:5,自引:0,他引:5
本文在较弱的条件下,研究了三阶奇异边值问题{x'+a(t)F(t,x)=0 0<t<1,x(0)=x'(0)=x(1)=0正解的存在性.允许非线性项a(t),F(t,x)在t=0,t=1及x=0处奇异. 相似文献
7.
8.
一类具有脉冲的非线性时滞微分方程解的渐进性 总被引:2,自引:0,他引:2
研究了-类具有脉冲的二阶非线性时滞微分方程 (r(t))X'-p(t)x'(t) n∑i=1 qi(t)x(t-σi) f(t)=0, t≠tk, x(t k)-x(tk)=akx(tk),x1(t k)-x1(tk)=bkx1(tk), k∈z 的解的渐近性,并得到了一系列相关的充分条件. 相似文献
9.
一类非线性二阶三点边值问题的单调迭代方法 总被引:4,自引:0,他引:4
姚庆六 《高等学校计算数学学报》2003,25(2):135-143
1 引言 本文的目的是对于下列非线性二阶常微分方程的三点边值问题建立正解迭代格式 (P)w~(11)(t)+f(t,w(t))=0,0≤t≤1,w(0)=0,aw(η)=w (1)其中0<η<1,0<α<1/η。这里问题(P)的正解w~*是指满足w~*(t)>0,0相似文献
10.
利用锥拉伸锥压缩不动点定理,证明了在一定条件下,下列非线性奇数阶方程(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,(-1)q+1u(2q+1)(t)=λa(t)f(u(t)),0 t 1,u(0)=u′(τ)=u″(1)=0u(2j+1)(0)=u(2j+1)(1)=0,j=1,2,…,q-1.单个和多个正解的存在性,其中λ>0,12<τ<1,q∈N.得到了λ的区间Λ,对一切λ∈Λ,该问题至少有一个正解,同样也得到了该问题至少有两个正解λ相应的区间. 相似文献
11.
Let (x) denote the number of those integers n with (n) x, where denotes the Euler function. Improving on a well-known estimate of Bateman (1972), we show that (x)-Ax R(x), where A=(2)(3)/(6) and R(x) is essentially of the size of the best available estimate for the remainder term in the prime number theorem. 相似文献
12.
Zachary Mesyan 《Semigroup Forum》2007,75(3):648-675
Let
be a countably infinite set,
the group of permutations of
, and
the monoid of self-maps of
. Given two subgroups
, let us write
if there exists a finite subset
such that the groups generated by
and
are equal. Bergman and Shelah showed that the subgroups which are closed in the function topology on S fall into exactly
four equivalence classes with respect to
. Letting
denote the obvious analog of
for submonoids of E, we prove an analogous result for a certain class of submonoids of E, from which the theorem for groups
can be recovered. Along the way, we show that given two subgroups
which are closed in the function topology on S, we have
if and only if
(as submonoids of E), and that
for every subgroup
(where
denotes the closure of G in the function topology in S and
its closure in the function topology in E). 相似文献
13.
B. P. Paneah 《Functional Analysis and Its Applications》2003,37(1):46-60
In this paper, some solvability problems for functional equations of the form
are studied. Here I is a finite closed interval in , F is an unknown continuous function,
and
are given continuous maps of I into itself, and
, and
are real-valued continuous functions on I. Such equations are of interest not only by themselves as an object of analysis, but they are also a necessary link in solving various problems in such diverse fields as integral and functional equations, measure theory, and boundary problems for hyperbolic differential equations. The major part of the proofs is based on the new results in the theory of dynamical systems generated by a noncommutative semigroup with two generators. 相似文献
14.
Let
be a continuous semimartingale and let
be a continuous function of bounded variation. Setting
and
suppose that a continuous function
is given such that F is C1,2 on
and F is
on
. Then the following change-of-variable formula holds:
where
is the local time of X at the curve b given by
and
refers to the integration with respect to
. A version of the same formula derived for an Itô diffusion X under weaker conditions on F has found applications in free-boundary problems of optimal stopping. 相似文献
15.
B. D. Sleeman E. M. E. Zayed 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1984,35(1):106-115
Summary The trace function
where {
m}
m=1
are the eigenvalues of the Laplacian is studied for a variety of domains. The dependence of(t) on the connectivity of a domain and the boundary conditions is analysed. Particular attention is given to annular domains.
Résumé Pour divers domaines, on étudie la fonction trace , où 1, 2, 3, sont les valeurs propres du laplacien. On analyse comment(t) dépend du domaine et des conditions aux limites. On considère notamment le cas de couronnes circulaires.相似文献
16.
In this paper, the concept of generalized-periodic solution is given for Riccati's equationy'=a(t)y
2+b(t)y+c(t) with perriodic coefficients, the relation between generalized-periodic solutions and the characteristic numbers of systemx'1=c(t)x
2,x'2=–a(t)x
1-b(t)x
2 is indicated, and several necessary and sufficient conditions are given using the coefficients. Moreover, in the case ofa(t) without zero, the relation between the number of continuous-periodic solutions ofy'=a(t)y
2+b(t)y+c(t)+ and the parameter is given; thus the problem on the existence of continuous-periodie solutions is basically solved. 相似文献
17.
ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.1.IntroductionInthispaper,weconsiderthefollowinginitial--boundaryvalueproblemwhereQ~fix(o,co),aQ=aflx(o,co),fiisaboundeddomaininEuclideanspaceR"(n22)withsmoothboundaryonandac=(u.,,'Iu..)denotesthegradientoffunctionu(x).Weassumethefunctionsal(x,t,u,p)(i=1,2,',n)anda(x,t,u,p)arelocallyH5ldercontinuousonfix(0,co)suchthatwherealtuandparepositiveconstants,m,aZIa3.hi,b2,alIadZ20,or321areconstants,m*E[0,m 2),hi16z/0,afl m*/… 相似文献
18.
本文研究退化时滞差分系统Ex(k+ 1)= Ax(k)+ ∑li= 1Bix(k- i)+ f(k) (k= 0,1,2,…),x(k)= φ(k) (k= 0,- 1,- 2,…,- l),其中E、A、Bi∈Rm ×n,x(k)∈Rn,f(k)∈Rm ,rank(E)< n.给出了上述系统解的存在性条件及通解表达式. 相似文献
19.
The following theorem is proved. Let {
k(t)} be an arbitrary complete orthonormal system on [0, 1] and let 1/2<<1. Then anf(t) C exists for all< such that
k=1
· |ck(f)|p=, p=2/(l+2), where
.Translated from Matematicheskie Zametki, Vol. 6, No. 5, pp. 567–572, November, 1969.The authors wish to thank P. P. Zabreiko and P. L. Ul'yanov for helpful discussions and remarks. 相似文献
20.
脉冲中立型时滞微分方程解的振动性 总被引:18,自引:0,他引:18
本文讨论一阶脉冲中立型时滞微分方程[y(t)+Py(t-σ)]′+Q(t)y(t-σ)=0,t0,t≠tk,k=1,2,…,y(t+k)-y(t-k)=bky(tk),k=1,2,…,{(E)这里τ,σ,P均为常数,τ>0,σ>0,Q(t)∈C([0,∞),R+),bk>-1,k=1,2,….分三种情况,P-1;-1<P<0;P>0给出了方程(E)所有解振动的充分条件. 相似文献