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1.
一类具不变性质的变系数偏微分方程的特解 总被引:1,自引:0,他引:1
In this paper, a few properties of general patial differential operator P beinginvariant with respect to the form F(|x|pp+|y|qq-|z|rr) are studied, where x∈Rn,y∈ Rm, z∈Rl.and explicit formulas are given for certain solution of the equation Pu=Aδ with P being a differential operator with power function coefficientswhich preserves the form (|x|pp+|y|qq-|z|rr)1/v for arbitrary even integers p, q, r,and odd integers v. 相似文献
2.
该文研究椭圆型方程
{Δpu+m|u|p-2u-Δqu+n|u|q-2u=g(x, u), x∈RN,
u∈ W1, p(RN)∩W1, q(RN)
弱解在全空间RN上的衰减性, 其中m, n ≥ 0, N≥3, 1 < q < p < N, g(x, u)关于u满足类渐近线性. 证明了该方程的
弱解在无穷远处关于|x|呈指数衰减性. 相似文献
3.
4.
本文讨论了二阶泛函微分方程的解的渐近性和振动性。文中指出,当sum from to +∞ (g-1)(1/(r(t))dt<+∞时,(1)式的非振动解的渐近性态有且仅有如下的四种类型:Ack,Ac∞,Aok,Ao∞。当sum from to +∞ (g-1)(1/(r(t))dt=+∞时,(1)式的非振动解的渐近性态有且仅有如下三种类型:Aco,A∞c,A∞c。在f为超线性或次线性的前提下,本文分别给出了存在Ack,Ac∞,Aok,Aco,A∞c等型非振动解的充要条件。在f为强超线性或强次线性的前提下,本文给出了方程(1)为振动的充要条件。 相似文献
5.
6.
7.
Let f(x) be a periodic function of period 2π,|f(x)|and |f(x)|p integrable on [0,2π].It is said to be f∈HX1,if (∫02π|f(x+h)-f(x)|pdx)1/p≤|h|.It is said to be f∈HX2,if (∫02π|f(x+h)+f(x-h)-2f(x)|pdx)1/p≤2|h|. 相似文献
8.
得到了算子在空间 Lp(Ωa,dvλ)(1< p< ∞)上有界的充分必要条件,其中h(ξ)=(1-|z|2)α-|w|2,Ks,u,v)( ξ , ξ'' )为一核函数.作为应用,证明了对所有多重指标α=( α1,…,αn)和β=(β1,…,βn),f∈LHp(Ωα, dvλ)蕴含1≤ p<∞. 相似文献
9.
关于Echelon空间无穷矩阵变换集的有界性 总被引:1,自引:1,他引:0
无穷矩阵变换是研究序列空间理论的重要工具.研究一个空间到另一个空间无穷矩阵变换的形式,是序列空间理论中的重要内容,并且已有众多工作.本文将进一步研究一般的Echelon空间到空间lp(1≤p≤∞),c、c0的无穷矩阵变换集的有界性.所得结果的特例正是Echelon空间到lp(1≤p≤∞)c、c0无穷矩阵变换的形式,同时概括了前人的许多结果. 相似文献
10.
Let Mn+p-1 denote the class of functions f(z) = 1/zp+a0/zp-2+a1/zp-2+…+an+p-1zn+…, regular and p-valent in the annulus 0<|z|<1 and satisfying Re((Dn+p f(z))/(Dn+p-1 f(z)))-2)<-(n+p-1)/(n+p),|z|<1,n>-p where Dn+p-1 f(z)=1/zp((zn+2p-1f(z))/(n+p-1)!)(n+p-1).Mn+p?Mn+p-1 is proved. Since M0 is the subclass of p-valent meromorphically starlike functions, all functions in Mn + p-1 are p-valent meromorphically star-like functions. Further the integrals of functions in Mn+p-1, are considered. 相似文献
11.
On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary 总被引:1,自引:0,他引:1
We consider nonnegative solutions of initial-boundary value problems for parabolic equationsu
t=uxx, ut=(um)xxand
(m>1) forx>0,t>0 with nonlinear boundary conditions−u
x=up,−(u
m)x=upand
forx=0,t>0, wherep>0. The initial function is assumed to be bounded, smooth and to have, in the latter two cases, compact support. We prove
that for each problem there exist positive critical valuesp
0,pc(withp
0<pc)such that forp∃(0,p
0],all solutions are global while forp∃(p0,pc] any solutionu≢0 blows up in a finite time and forp>p
csmall data solutions exist globally in time while large data solutions are nonglobal. We havep
c=2,p
c=m+1 andp
c=2m for each problem, whilep
0=1,p
0=1/2(m+1) andp
0=2m/(m+1) respectively.
This work was done during visits of the first author to Iowa State University and the Institute for Mathematics and its Applications
at the University of Minnesota. The second author was supported in part by NSF Grant DMS-9102210. 相似文献
12.
Chin-Cheng Lin 《分析论及其应用》2001,17(2):45-53
Let f∈L p (R), 1≤p≤t8, and c j be the inner product of f and the Hermite function h j . Assume that c j 's satisfy $\left| {c_j } \right| \cdot f = o\left( 1 \right)\;\quad as\;j \to \infty $ If r=5/4, then the Hermite series Σc j h j conerges to f almost everywhere. If r=9/4-1/p, the Σ c j h j converges to f in L p (R). 相似文献
13.
Cp 总被引:1,自引:0,他引:1
Charles A. McCarthy 《Israel Journal of Mathematics》1967,5(4):249-271
The spacec
p is the class of operators on a Hilbert space for which thec
p norm |T|
p
=[trace(T*T)
p/2]1/p
is finite. We prove many of the known results concerningc
p in an elementary fashion, together with the result (new for 1<p<2) thatc
p is as uniformly convex a Banach space asl
p. In spite of the remarkable parallel of norm inequalities in the spacesc
p andl
p, we show thatp ≠ 2, noc
p built on an infinite dimensional Hilbert space is equivalent to any subspace of anyl
p orL
p space.
The author was supported by National Science Foundation Grant GP-5707. 相似文献
14.
LetA={a
1, …,a
k} and {b
1, …,b
k} be two subsets of an abelian groupG, k≤|G|. Snevily conjectured that, when |G| is odd, there is a numbering of the elements ofB such thata
i+b
i,1≤i≤k are pairwise distinct. By using a polynomial method, Alon affirmed this conjecture for |G| prime, even whenA is a sequence ofk<|G| elements. With a new application of the polynomial method, Dasgupta, Károlyi, Serra and Szegedy extended Alon’s result to
the groupsZ
p
r
andZ
p
rin the casek<p and verified Snevily’s conjecture for every cyclic group. In this paper, by employing group rings as a tool, we prove that
Alon’s result is true for any finite abelianp-group withk<√2p, and verify Snevily’s conjecture for every abelian group of odd order in the casek<√p, wherep is the smallest prime divisor of |G|.
This work has been supported partly by NSFC grant number 19971058 and 10271080. 相似文献
15.
In this short note we prove that if 1 < c < 81/40, c ≠ 2, N is a large real number, then the Diophantine inequality
|p1c+p2c+p3c+p4c+p5c-N| < log-1 N \vert p_1^c+p_2^c+p_3^c+p_4^c+p_5^c-N\vert < \log^{-1} N
is solvable, where p
1,···,p
5 are primes. 相似文献
16.
Chunije Wang 《Mathematische Nachrichten》2008,281(3):447-454
Let Ap (??) (p ≥ 1) be the Bergman space over the open unit disk ?? in the complex plane. Korenblum's maximum principle states that there is an absolute constant c ∈ (0, 1) (may depend on p), such that whenever |f (z)| ≤ |g (z)| (f, g ∈ Ap (??)) in the annulus c < |z | < 1, then ∥f ≤ ∥g ∥. For p ≥ 1, let cp be the largest value of c for which Korenblum's maximum principle holds. In this note we prove that cp → 1 as p → ∞. Thus we give a positive answer of a question of Hinkkanen. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
Christian Borgs Jennifer T. Chayes Remco van der Hofstad Gordon Slade Joel Spencer 《Random Structures and Algorithms》2005,27(2):137-184
We study random subgraphs of an arbitrary finite connected transitive graph ?? obtained by independently deleting edges with probability 1 ? p. Let V be the number of vertices in ??, and let Ω be their degree. We define the critical threshold pc = pc (??, λ) to be the value of p for which the expected cluster size of a fixed vertex attains the value λV1/3, where λ is fixed and positive. We show that, for any such model, there is a phase transition at pc analogous to the phase transition for the random graph, provided that a quantity called the triangle diagram is sufficiently small at the threshold pc. In particular, we show that the largest cluster inside a scaling window of size |p ? pc| = Θ(Ω?1V?1/3) is of size Θ(V2/3), while, below this scaling window, it is much smaller, of order O(??2 log(V?3)), with ? = Ω(pc ? p). We also obtain an upper bound O(Ω(p ? pc)V) for the expected size of the largest cluster above the window. In addition, we define and analyze the percolation probability above the window and show that it is of order Θ(Ω(p ? pc)). Among the models for which the triangle diagram is small enough to allow us to draw these conclusions are the random graph, the n‐cube and certain Hamming cubes, as well as the spread‐out n‐dimensional torus for n > 6. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005 相似文献
18.
On Hua-Tuan’s conjecture 总被引:2,自引:0,他引:2
Let G be a finite group and |G| = pn, p be a prime. For 0 m n, sm(G) denotes the number of subgroups of of order pm of G. Loo-Keng Hua and Hsio-Fu Tuan have ever conjectured: for an arbitrary finite p-group G, if p > 2, then sm(G) ≡ 1, 1 + p, 1 + p + p2 or 1 + p + 2p2 (mod p3). In this paper, we investigate the conjecture, and give some p-groups in which the conjecture holds and some examples in which the conjecture does not hold. 相似文献
19.
Patrick J. Rabier 《Journal d'Analyse Mathématique》2012,118(1):251-296
We characterize all the real numbers a, b, c and 1 ?? p, q, r < ?? such that the weighted Sobolev space $$W_{\{ a,b\} }^{\{ q,q\} }({R^N}\backslash \{ 0\} ): = \{ u \in L_{loc}^1({R^N}\backslash \{ 0\} ):{\left| x \right|^{a/q}} \in {L^q}({R^{N),}}{\left| x \right|^{b/p}}\nabla u \in {({L^p}({R^N}))^N}\} $$ is continuously embedded into $${L^r}({R^N};{\left| x \right|^c}dx): = \{ u \in L_{loc}^1({R^N}\backslash \{ 0\} ):{\left| x \right|^{c/r}}u \in {L^r}({R^N})\} $$ with norm ??·?? c,r . It turns out that, except when N ?? 2 and a = c = b ? p = ?N, such an embedding is equivalent to the multiplicative inequality $${\left\| u \right\|_{c,r}} \le C\left\| {\nabla u} \right\|_{b,p}^\theta \left\| u \right\|_{a,q}^{1 - \theta }$$ for some suitable ?? ?? [0, 1], which is often but not always unique. If a, b, c > ?N, then C 0 ?? (? N ) ? W {a,b} (q,p) (? N {0}) ?? L r (? N ; |x| c dx) and such inequalities for u ?? C 0 ?? (? N ) are the well-known Caffarelli-Kohn-Nirenberg inequalities; but their generalization to W {a,b} (q,p) (? N {0}) cannot be proved by a denseness argument. Without the assumption a, b, c > ?N, the inequalities are essentially new, even when u ?? C 0 ?? (? N {0}), although a few special cases are known, most notably the Hardy-type inequalities when p = q. In a different direction, the embedding theorem easily yields a generalization when the weights |x| a , |x| b and |x| c are replaced with more general weights w a ,w b and w c , respectively, having multiple power-like singularities at finite distance and at infinity. 相似文献
20.
W. Mader 《Journal of Graph Theory》2002,39(2):129-144
Let |D| and |D|+n denote the number of vertices of D and the number of vertices of outdegree n in the digraph D, respectively. It is proved that every minimally n‐connected, finite digraph D has |D|+n ≥ n + 1 and that for n ≥ 2, there is a cn > 0 such that for all minimally n‐connected, finite digraphs D. Furthermore, case n = 2 of the following conjecture is settled which says that every minimally n‐connected, finite digraph has a vertex of indegree and outdegree equal to n. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 129–144, 2002 相似文献