具有凸凹项非齐次拟线性椭圆方程的多解性

在Orlicz—Sobolev空间中利用临界点理论考虑了非齐次拟线性椭圆方程{-div((︱▽u︱)▽u)=μ︱u︱q-2u+λ︱u︱p-2u在Ω中,u=0在Ω上无穷多解的存在性,其中Ω是R~N中边界光滑的有界区域,μ,λ∈R是两个参数.     

一类拟线性椭圆方程的多重解

利用变分法和一个三临界点定理,证明了一类拟线性椭圆方程-div(a|u|p)|u|p-2u)=λf(x,u),u=0,ΩΩ,在某些新的条件下至少存在三个解,其中ΩRn(n≥1)是一个具有光滑边界的有界区域,且a∈C(R ,R),p>n,λ>0为一实参数.并给出了该结论在毛细现象中的广义Capillarity方程的一个应用.     

p-Laplace方程正解的存在性和多重性

这篇文章讨论边值问题-(| u′|p-2u′)′=λf(t ,u) ,t∈(0,1) ,p >1,u(0) =u(1) =0,其中f(t ,u)≥-M( M是正常数) ,对(t ,u)∈0,1×0,∞) .我们利用度理论和锥上的不动点定理得到方程存在两个正解.     

奇数阶边值问题正解的存在性与多重性

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.     

一类带Hardy-Sobolev临界指数的奇异Kirchhoff型方程正解的存在性

本文研究了一类带Hardy-Sobolev临界指数的奇异Kirchhoff型{-(a+b∫_Ω︱▽u︱~2dx)△u=u~(5-2s)/︱x︱~s+λu~(-γ),x∈Ω,u0,x∈Ω,u=0,x∈δΩ方程其中ΩR~3是一个有界开区域且具有光滑边界δΩ,0∈Ω,a,b≥0且a+b0,λ0,0γ1,0≤s1.利用变分方法,获得了该问题的一个正局部极小解,补充了文献[1]的结果.     

临界非齐次双调和方程的多解存在性

该文讨论了下列边值问题Δ2 u =λu |u|p- 1u μf (x) ,x∈Ω ,μ >0 ;u| Ω =0 , u n Ω =0 .的多解存在性和非存在性 .其中 :Ω RN是有界光滑区域 ,N≥ 5,λ∈ R1,P =N 4N - 4,f(x)是Ω中的非负不恒为零的连续函数 ,Δ2 =ΔΔ表示 N维双调和算子 .     

Carathodory条件下超线性半正边值问题的正解

本文不要求非线性项 f( t,u)连续且下方有界 ,在 f 满足 Carathéodory条件下 ,证明了半正的 Sturm-Liouville边值问题( p( t) u′)′ λf ( t,u) =0 ,r0存在正解 .这里半正是指 ,允许非线性项取负值     

次线性半正边值问题的正解

本文讨论 Sturm-Liouville边值问题(p(t)u′)′+λf(t,u)=0, r＜t＜R;au(r)-bp(r)u′(r)=0;cu(R)+dp(R)u′(R)=0,正解的存在性,这里允许非线性项取负值．当f在u=+∞处一致次线性增长且无界时，必存在λ^*＞0，对?λ:λ＞λ^*,上述边值问题存在正解．     

一类p-Laplacian方程单侧全局区间分歧及应用

首先建立一类含不可微非线性项p-Laplacian方程的单侧全局区间分歧定理.应用上述定理,可以证明一类半线性p-Laplacian方程主半特征值的存在性.进而,可研究下列半线性p-Laplacian方程结点解的存在性{-(r~(N-1)φp(u'))'=α(r)r~(N-1)φp(u~+)+β(r)r~(N-1)φp(u~-)+λα(r)r~(N-1)f(u),a.e.r∈(0,1) u'(0)=u(1)=0,其中1p+∞,φ_p(s)=|s|~(p-2)s,a(r)∈C[0,1],a(r)≥0且在[0,1]的任何子集上成立a(r)≠0;λ是一个参数,u~+=max{u,0},u~-=-min{u,0},α,β∈C[0,1];对于s∈R~+,都有f∈C(R,R)且sf(s)0,R~+=[0,+∞),并且满足f_0∈[0,∞)且f_∞∈(0,∞)或者f_0∈(0,∞]且f_∞=0或者f_0=0且f_∞=∞,其中f_0=lim︱8︱→0 f(s)/s,f_∞=f_0=lim︱8︱→+∞ f(s)/s该文用单侧全局分歧技巧和连通分支极限证明结论.     

非线性双曲型方程的混合元方法

1　引　　言考虑下述非线性双曲型方程的混合问题:c(x,u)utt-.(a(x,u)u)=f(x,u,t),　　x∈Ω,t∈J,(1.1)u(x,0)=u0(x),　　x∈Ω,(1.2)ut(x,0)=u1(x),　　x∈Ω,(1.3)u(x,t)=-g(x,t),　　(x,t)∈Ω×J,(1.4)其中ΩR2是一具有Lipschitz边界Ω的有界区域,J=[0,T],0相似文献   

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the comparison between the APV and the NPV computed via the WACC

The valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of the APV is available. The paper shows that the APV can be interpreted as the arbitrage free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation, generally different from the APV, allows for arbitrage. We provide various conditions which completely characterize the sign of the error as a functions of all the variables entering the model.     

用常微分方程模型分析预防和隔离措施对SARS发病率的影响

通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 .     

On the Gap in the Spectrum of the Translations

The spectrum of the translations in local quantum field theory will be analyzed in order to show that in a positive energy representation without vacuum vector and with lowest mass m₁ there is no gap in the spectrum which is larger than 2m₁. In particular in a zero mass representation there is no hole at all. These results are obtained with methods of analytic functions of several complex variables.     

From the subalgebras of the square to the discriminator

Presented by A. F. Pixley.     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

On the depth of the tangent cone and the growth of the Hilbert function

For a dimensional Cohen-Macaulay local ring we study the depth of the associated graded ring of with respect to an -primary ideal in terms of the Vallabrega-Valla conditions and the length of , where is a minimal reduction of and . As a corollary we generalize Sally's conjecture on the depth of the associated graded ring with respect to a maximal ideal to -primary ideals. We also study the growth of the Hilbert function.

     

On the Decomposition of the Riesz Operator and the Expansion of the Riesz Semigroup

For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues denote by E(λ_i; T) the eigen-projection corresponding to an eigenvalue λ_i. In this paper we will show that if the operator sequence is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators T_p and T_r: T = T_p + T_r, where T_p is the weak limit of T_n and T_r is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t ≥ τ. As an application, we consider the solution of transport equation on a bounded convex body.