共查询到10条相似文献,搜索用时 15 毫秒
1.
定理 设数列{αn}是等差数列,sn=α1^m+α2^m+…+αn^m,m∈N^*,则存在λi∈R(i=2,3,…,m+1),有g(n)=λm+1αn^m+1+λmαn^m+…+λ3αn^3+λ2αn^2,使{sn-g(n)}为等差数列. 相似文献
2.
MOUSSAOUI Abdelkrim KHODJA Brahim 《偏微分方程(英文版)》2009,22(2):111-126
In this paper, we study the existence of nontrivial solutions for the problem
{-△u=f(x,u,v)+h1(x)in Ω
-△v=g(x,u,v)+h2(x)inΩ
u=v=0 onδΩ
where Ω is bounded domain in R^N and h1,h2 ∈ L^2 (Ω). The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g:
{lim s,|t|→+∞f(x,s,t)/s=lim |s|,t→+∞g(x,s,t)/t=λ+1 uniformly on Ω,
lim -s,|t|→+∞f(x,s,t)/s=lim |s|,-t→+∞g(x,s,t)/t=λ-,uniformly on Ω,
where λ+,λ-∈(0)∪σ(-△),σ(-△)denote the spectrum of -△. The cases (i) where λ+ = λ_ and (ii) where λ+≠λ_ such that the closed interval with endpoints λ+,λ_ contains at most one simple eigenvatue of -△ are considered. 相似文献
{-△u=f(x,u,v)+h1(x)in Ω
-△v=g(x,u,v)+h2(x)inΩ
u=v=0 onδΩ
where Ω is bounded domain in R^N and h1,h2 ∈ L^2 (Ω). The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g:
{lim s,|t|→+∞f(x,s,t)/s=lim |s|,t→+∞g(x,s,t)/t=λ+1 uniformly on Ω,
lim -s,|t|→+∞f(x,s,t)/s=lim |s|,-t→+∞g(x,s,t)/t=λ-,uniformly on Ω,
where λ+,λ-∈(0)∪σ(-△),σ(-△)denote the spectrum of -△. The cases (i) where λ+ = λ_ and (ii) where λ+≠λ_ such that the closed interval with endpoints λ+,λ_ contains at most one simple eigenvatue of -△ are considered. 相似文献
3.
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
4.
SUN Fuqin LI Fan JIA Xiuqing 《偏微分方程(英文版)》2009,(3):282-298
In this paper, we study the higher-order semilinear parabolic system{ut+(-△)^mu=a|v|^p-1v,(t,x)∈R^1+×R^N,vt+(-△)^mv=b|u|^q-1u,(t,x)∈R^1+×R^N,u(0,x)=φ(x),v(0,x)=ψ(x),x∈R^N, where m, p,q 〉 1, a,b ∈R. We prove that the global existence of mild solutions for small initial data with respect to certain norms. Some of these solutions are proved to be asymptotically self-similar. 相似文献
5.
Linghai ZHANG 《数学年刊B辑(英文版)》2008,29(2):179-198
Let u=u(x,t,uo)represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt+δux+γHuxx+βuxxx+f(u)x=αuxx,u(x,0)=uo(x), whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f(0)=0,|f(u)|→∞as |u|→∞,and f∈C^1(R),and there exist the following limits Lo=lim sup/u→o f(u)/u^3 and L∞=lim sup/u→∞ f(u)/u^5 Suppose that the initial function u0∈L^I(R)∩H^2(R).By using energy estimates,Fourier transform,Plancherel's identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv(xxt)+δvx+γHv(xx)+βv(xxx)=αv(xx),v(x,0)=vo(x), the author justifies the following limits(with sharp rates of decay) lim t→∞[(1+t)^(m+1/2)∫|uxm(x,t)|^2dx]=1/2π(π/2α)^(1/2)m!!/(4α)^m[∫R uo(x)dx]^2, if∫R uo(x)dx≠0, where 0!!=1,1!!=1 and m!!=1·3…(2m-3)…(2m-1).Moreover lim t→∞[(1+t)^(m+3/2)∫R|uxm(x,t)|^2dx]=1/2π(x/2α)^(1/2)(m+1)!!/(4α)^(m+1)[∫Rρo(x)dx]^2, if the initial function uo(x)=ρo′(x),for some functionρo∈C^1(R)∩L^1(R)and∫Rρo(x)dx≠0. 相似文献
6.
下面的定理肯定了一致连续函数的积分体系唯一性.
命题 5(一致连续函数的积分体系唯一性) 设f(x)在区间I的任一个闭子区间上一致连续,S(u,v)和R(u,v)都是f(x)在I上的积分体系,则恒有S(u,v)=R(u,v). 相似文献
7.
设G是n阶2-连通图,3≤c≤n.本文绘出对于图G的每一个同构于K1.3或Z1的导出子图L,若d(u)且如果dL(u,v)=2有(v)=min{,|M3(u)|/2}这里M3(u)={v|dc(u,v)≤3},则G包含长至少为c的圈. 相似文献
8.
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.
In this paper we consider the bifurcation problem -div A(x, u)=λa(x)|u|^p-2u+f(x,u,λ) in Ω with p 〉 1.Under some proper assumptions on A(x,ξ),a(x) and f(x,u,λ),we show that the existence of an unbounded branch of positive solutions bifurcating Irom the principal eigenvalue of the problem --div A(x, u)=λa(x)|u|^p-2u. 相似文献