共查询到20条相似文献,搜索用时 515 毫秒
1.
证明了:对任一在Cn中超球Bn上可微的(0,q)式g(z)若适合g=0,而且g在Bn内有紧致的支集,则当n≥q 1时v(w)=*∫Bng(z)∧*zN(z,w)是方程v=g之解,它在边界Bn上为零. 相似文献
2.
证明了:对任一在Cn中超球Bn上可微的(0,q)式g(z)若适合(-e)g=0,而且g在Bn内有紧致的支集,则当n≥q+1时v(w)=(-e)*∫Bng(z)∧*z—N(z,w)是(-e)方程(-e)v=g之解,它在边界Bn上为零. 相似文献
3.
In this paper, we study how the shape of the graph of a(z) affects on the number of positive solutions of -△v+μb(z)v=a(z)vp-1+λh(z)vq-1,inRN.(0.1) We prove for large enough λ,μ〉 0, there exist at least k+ 1 positive solutions of the this semilinear elliptic equations where 1 ≤ q 〈 2 〈 p 〈 2* = 2N/(N-2) forN ≥ 3. 相似文献
4.
We consider the properties on solutions of some q-difference equations of the form ∑ n j=0 aj(z)f(qj z)=an+1(z), where a0(z),..., an+1(z) are meromorphic functions, a0(z)an(z) ≠ 0 and q ∈ C such that 0 〈 |q| ≤ 1. We give estimates on the upper bound for the length of the gap in the power series of entire solutions of (*) when the coefficients a0(z),..., an+1(z) are polynomials and 0 〈 |q| 〈 1. For some special cases, we give estimates of growth of f(z). And we also show that the case 0 〈 |q| 〈 1 is different from the case |q|=1. 相似文献
5.
RESEARCH ANNOUNCEMENTS——Dynamical Behavior for the Three-dimensional Generalized Hasegawa-Mima Equations 总被引:1,自引:0,他引:1
We consider the following generalized three-dimensional (3-D) dissipative Hasegawa-Mima equations:
△ut - ut + {u, △u} + knuy - vz + α△(u - △u) + f(x, y, z) = 0, (1)
vt + {u, v} + uz + γv - β△v = g(x, y, z) (2)
with initial datum
v|t=0=u0(x,y,z),v|t=0=v0(x,y,z),(x,y,z)∈Ω∈R^3 (3). 相似文献
6.
LI Junfeng LIU Weian 《偏微分方程(英文版)》2009,(3):266-281
This paper is concerned with the asymptotic behavior of solution to the following model involving two species all with chemotaxis:{αp/αt=Dp△(p△lnp/w),αp/αt=Dq△(q△lnq/w),αw/αt=βp-δw,p△ln(p/w).^-n=q△ln(q/w).^-n=0.We prove that the solution exists globally asβ ≥ 0. Asβ 〈 0, whether the solution exists globally or not depends on the initial data. By function transformation and compari- son, the asymptotical behavior of the solution is studied. 相似文献
7.
Using variational methods, we prove the existence of a nontrivial weak solution for the problem
{-∑i=1^Nδxi(|δxiu|pi-2δxiu)=λα(x)|u|q(x)-2u+|u|p*-2u,in Ω,
u=0 inδΩ,
where Ω R^N(N≥3) is a bounded domain with smooth boundary δΩ,2≤pi〈N,i=1,N,q:Ω→(1,p*)is a continuous function, p* =N/∑i=1^N 1/pi-1 is the critical exponent for this class of problem, and λ is a parameter. 相似文献
{-∑i=1^Nδxi(|δxiu|pi-2δxiu)=λα(x)|u|q(x)-2u+|u|p*-2u,in Ω,
u=0 inδΩ,
where Ω R^N(N≥3) is a bounded domain with smooth boundary δΩ,2≤pi〈N,i=1,N,q:Ω→(1,p*)is a continuous function, p* =N/∑i=1^N 1/pi-1 is the critical exponent for this class of problem, and λ is a parameter. 相似文献
8.
在区域Ω上考虑一类由退化向量场形成的Schrodinger方程:
∑i,j=1^mXi^*(aij(x)Xju)-vu=0
其中X1,…,Xm为R^n(n≥)3上满足Hormander条件的实C^∞向量场,Xi^*为Xi的形式共轭,v属于Kato类的某一类比Kη^loc(Ω).并得到以下结果:若u为以上方程的弱解,则|Xu|^2w=∑i=1^m|Xiu|^2w∈Kη^loc(Ω). 相似文献
9.
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(v)=|v|p-2v1 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
10.
Let Ω IR^N, (N ≥ 2) be a bounded smooth domain, p is Holder continuous on Ω^-,
1 〈 p^- := inf pΩ(x) ≤ p+ = supp(x) Ω〈∞,
and f:Ω^-× IR be a C^1 function with f(x,s) ≥ 0, V (x,s) ∈Ω × R^+ and sup ∈Ωf(x,s) ≤ C(1+s)^q(x), Vs∈IR^+,Vx∈Ω for some 0〈q(x) ∈C(Ω^-) satisfying 1 〈p(x) 〈q(x) ≤p^* (x) -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^+ ≤ q- ≤ q+. As usual, p* (x) = Np(x)/N-p(x) if p(x) 〈 N and p^* (x) = ∞- if p(x) if p(x) 〉 N. Consider the functional I: W0^1,p(x) (Ω) →IR defined as
I(u) def= ∫Ω1/p(x)|△|^p(x)dx-∫ΩF(x,u^+)dx,Vu∈W0^1,p(x)(Ω),
where F (x, u) = ∫0^s f (x,s) ds. Theorem 1.1 proves that if u0 ∈ C^1 (Ω^-) is a local minimum of I in the C1 (Ω^-) ∩C0 (Ω^-)) topology, then it is also a local minimum in W0^1,p(x) (Ω)) topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation (P) defined below. 相似文献
1 〈 p^- := inf pΩ(x) ≤ p+ = supp(x) Ω〈∞,
and f:Ω^-× IR be a C^1 function with f(x,s) ≥ 0, V (x,s) ∈Ω × R^+ and sup ∈Ωf(x,s) ≤ C(1+s)^q(x), Vs∈IR^+,Vx∈Ω for some 0〈q(x) ∈C(Ω^-) satisfying 1 〈p(x) 〈q(x) ≤p^* (x) -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^+ ≤ q- ≤ q+. As usual, p* (x) = Np(x)/N-p(x) if p(x) 〈 N and p^* (x) = ∞- if p(x) if p(x) 〉 N. Consider the functional I: W0^1,p(x) (Ω) →IR defined as
I(u) def= ∫Ω1/p(x)|△|^p(x)dx-∫ΩF(x,u^+)dx,Vu∈W0^1,p(x)(Ω),
where F (x, u) = ∫0^s f (x,s) ds. Theorem 1.1 proves that if u0 ∈ C^1 (Ω^-) is a local minimum of I in the C1 (Ω^-) ∩C0 (Ω^-)) topology, then it is also a local minimum in W0^1,p(x) (Ω)) topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation (P) defined below. 相似文献
11.
12.
Bohr's type inequalities are studied in this paper: if f is a holomorphic mapping from the
unit ball B^n to B^n, f(0)=p, then we have sum from k=0
to∞|DφP(P)[D^kf(0)(z^k)]|/k!||DφP(P)||〈1 for|z|〈max{1/2+|P|,(1-|p|)/2^1/2andφ_P
∈Aut(B^n) such thatφ_(p)=0. As corollaries of the above estimate, we obtain some sharp Bohr's type
modulus inequalities. In particular, when n=1 and |P|→1, then our theorem reduces to a classical
result of Bohr. 相似文献
13.
含零点弧的双解析函数在极点处的性质 总被引:1,自引:0,他引:1
In this paper, the properties of bianalytic functions w(z) = z^-Ф1(z) +Ф2(z) with zero arc at the pole z = 0 are discussed. Some conditions under which there exists an arc γ, an end of which is z = 0, such that w(z) =0 for arbitary z ∈γ/{0} are given. Secondly, that the limit set of w(z) is a circle or line as z → 0 is proved in this case. Finally, two numerical examples are given to illustrate our results. 相似文献
14.
In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H(B^n) satisfying ||f||0 = 1 and det f'(0) = α ∈ (0, 1], where||f||0 = sup{(1 - |z|^2 )n+1/2n det(f'(z))[1/n : z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f(0). When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara. 相似文献
15.
<正> Ⅰ.引言1.设 w=f(z)是 z 平面上的亚纯函数,z=g(w)是 f(z)的反函数,F 是 g(w)的黎曼曲面.再设(w_0)是 F 的一个可近边界点.(w_0)在 w 平面上的投影为 w_0 点.于是在 z 平面上有一条相应的伸展到∞的连续曲线 L,使得 相似文献
16.
讨论边值问题((一v'(r))~n)'=λ(v~α+v~β),v'(0)=v(1)=0,其中λ〉0是正参数.对(n-α)(n-β)〉0的情形得出了正解的存在唯一性.对0〈α〈n〈β的情形得到,存在λ~*〉0,使得当0〈λ〈λ~*时,此边值问题恰好存在两个正解;当λ=λ~*时,此边值问题存在唯一一个正解;当λ〉λ~*时,此边值问题不存在正解. 相似文献
17.
对解析函数f(z)=p(z)/q(z),当z=a分别是p(z)和q(z)的m级零点和n级零点,且0≤m<n时,特别地n=m+2时,讨论了求f(z)在极点z=a处留数的方法并举例说明其应用. 相似文献
18.
A Mendelsohn triple system of order v (MTS(v)) is a pair (X,B) where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS(v) (X,B) is called pure and denoted by PMTS(v) if (x, y, z) ∈ B implies (z, y, x) ∈B. A large set of MTS(v)s (LMTS(v)) is a collection of v - 2 pairwise disjoint MTS(v)s on a v-set. A self-converse large set of PMTS(v)s, denoted by LPMTS* (v), is an LMTS(v) containing [ v-2/2] converse pairs of PMTS(v)s. In this paper, some results about the existence and non-existence for LPMTS* (v) are obtained. 相似文献
19.
Wen Jiwei Yan Yunliang 《高校应用数学学报(英文版)》2006,21(1):87-95
Let X,X1,X2 be i. i. d. random variables with EX^2+δ〈∞ (for some δ〉0). Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ* (n)=supx∈zζ(x,n),ζ(x,n) =#{0≤k≤n:[Sk]=x}. A strong approximation of ζ(n) by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ*(n) are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ*(n) is proved. 相似文献
20.
方爱农 《数学年刊A辑(中文版)》1982,(5)
前言 本文研究一阶非线性椭圆型方程组——方程组(A). w_z=g(z,w,w_(?)), (A,1) |g(z,w,w_z~1)-g(z,w,w_z~2)|≤q_0|w_z~1-w_z~2|,q_0=常数<1 (A,2) 的下列两类典型的边值问题: 问题P(或H) 在单位圆G内寻求方程组(A)的解w(z),而且在|z|=1上满足边 相似文献