Maximum Principle of Semi-Linear Distributed System (I)

In this paper, an optimal control problem of non-linear Volterra systems $x(\cdot)=h(t)+\int_0^t G(t,s)f(s,x(s),u(s))ds$ on Banach space X with a general cost functional $Q(u(\cdot)) = \int_0^T J(s,x(s,u(\cdot)),u(s))ds$ is discussed, where $G(t,s)\in \varphi(X)$ is strongly continuous in (t, s), h(\cdot)\in C([0,T],G),f(s,x,u):[0,T]*X*U \rightarrow X and J (s, x, u) : [0, T] *X*U \rightarrow R. The control region U is an arbitrary set in a Banach space. Under some other assumptions of f and J, we have proved the following Theorem. The optimal control u^*(\cdot) of the above problem satisfies max $H(t,u)=H(t,u^*(t))$ for a.e.t\in [0,T], Where $H(t,u)=-J(t,x^*(t),u)+(\phi(t),f(t,x^*(t),u))$, $\phi(t)=\int_t^T J_x(s,x^*(s),u^*(s))U(s,t)ds$ and $x^*(t)=x(t,u^*(\cdot)),U(s,t)\in \phi(X)$ is the solution of $U(s,t)=G(s,t)+\int _t^s G(s,w)f_x(w,x^*(w),u^*(w))U(w,t)dw$. We have applied the results to semi-linear distributed systems.     

带一类时滞项的生物种群扩散模型的行波解

本文利用Schauder不动点理论证明了微分积分方程组行波解u（x，t）＝U（z）,w（x,t）＝W（z）,z＝xγ－ct的存在性．这个方程组描述了一类在植物上繁殖，且靠飞行在空中扩散的生物种群扩散过程．特别当时滞项，中积分核K（t）（反映种群繁殖模式）属于L1（0，∞）时，本文得到极限值W（－∞）（表示最终植物上种群密度）小于M．这个结论较符合生物实际．     

一类含隅角和弯矩的奇异梁方程三个正解的存在性

利用格林函数方法和Avery-Peterson不动点定理研究了一类非线性四阶两点边值问题u(4)(t) =f(t,u(t),u′(t),u″(t)), 0 ＜ t ＜ 1,u(0) =u′(1) =u″(0) =u′″(1) =0多个正解的存在性,其中允许非线性项f(t,u,v,w)在t=0,t=1,u=0,v=0,w=0处奇异.在力学上该问题模拟了左端简单支撑右端被滑动夹子夹住的弹性梁的挠曲.由于非线性项同时涉及隅角和弯矩,因此主要结论对于梁的稳定性分析是有益的.最后我们给出了一个例子,进一步证实本文理论的严密性和可行性.     

Distribution function of the absolute maximum of random harmonic oscillations

An analytical expression is derived for the distribution function of the absolute maximum of a Gaussian stationary process with correlation function p(t)=₁ ²+₂ ²cost t.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 144–147, 1986.     

On Quasi-Polarized Surfaces of General Type Whose Sectional Genus is Equal to the Irregularity

Let (X,L) be a quasi-polarized surface over the complex number field. In this paper, we classified quasi-polarized surfaces (X,L) with g(L)=q(X), (X)=2, and h0(L)>0.     

测度链上p-Laplacian 边值问题的三个正对称解

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.     

奇异三阶两点边值问题解的一个存在定理

By constructing suitable Banach space.an existence theorem is established under a condition of linear growth for the third-order boundary value problem u'"(t) f(t,u(t),t'(t),u"(t))=0,0＜t＜1,u(0)=u'(0)=u'(1)=0,where the nonlinear term contains first and second derivatives of unknown function.In this theorem the nonlinear term f(t,u,v,w)may be singular at t=0 and t=1.The main ingredient is Leray-Schauder nonlinear alternative.     

Explicit expression for the transition density of the solution of a stochastic diffusion equation with piecewise-constant drift coefficient

The explicit form of the transition density is determined for the solution (t) of the stochastic diffusion equation d(t)=a((t))dt+dw(t), where a(z)= for x [a, b] and a(x)=0 for x [a, b], w(t) is a Wiener process.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 99–105, 1987.     

二阶常微分方程Robin边值问题正解的存在性

基于锥理论,研究了二阶常微分方程Robin边值问题u″+h(t)u′+f(t,u)=0,t∈(a,b),u(a)=0,u′(b)=0,0相似文献   

一类n-阶m-点奇异边值问题的正解

研究n-阶m-点奇异边值问题其中h(t)允许在t=0,t=1处奇异,f(t,v_0,v_1,…,v_(n-2))允许在v_i=0(i=0,1,…,n-2)处奇异.利用锥拉伸与压缩不动点定理得到了上述奇异边值问题正解的存在性.     

On Perturbed Discrete Boundary Value Problems

In this paper, we study nonlinear discrete boundary value problems of the form x ( t +1)= A ( t ) x ( t )+ h ( t )+ k f ( t , x ( t ), k ) subject to Bx (0)+ Dx ( J )= u + k g ( x (0), x ( J ), k ) where k is a "small" parameter. Our main concern is the case of resonance, that is, the situation where the associated linear homogeneous boundary value problem x ( t +1)= A ( t ) x ( t ), Bx (0)+ Dx ( J )=0 admits nontrivial solutions. We establish conditions for the solvability of the nonlinear boundary value problem when k is "small". We also establish qualitative properties of these solutions.     

抽象空间中非时齐马氏过程的分析理论(Ⅱ)——非时齐马氏过程与双参数半群

本文是[1]的续篇,一切符号及定义均沿袭[1].为省篇幅,不再重述.     

非线性中立型微分差分方程非振动解的渐近性

考虑非线性中立型微分差分方程［ｙ（ｔ）＋Ｐ（ｔ）ｇ（ｙ（ｔ－τ）］′＋Ｑ（ｔ）ｈ（ｙ（ｔ－σ））＝０（１）的非振动解的渐近性．若无特别申明，本文总假设Ａ函数Ｐ（ｔ），Ｑ（ｔ），ｇ（ｕ），ｈ（ｕ）皆为连续函数；ＢＱ（ｔ）＞０；ｕｇ（ｕ）＞０，ｕｈ（ｕ）＞０（ｕ≠０）；Ｃｇ（ｕ）＝ｈ（ｕ）＝０当且仅当ｕ＝０．     

二阶奇异初值问题正解

应用不动点定理和逼近方法,研究了二阶非线性奇异初值问题正解的存在性,获得了若干新结果。     

On Variation of Single Birth Processes

Suppose {X（t）; t≥ 0} is a single birth process with birth rate qii＋l （i 〉 0） and death rate qij （i 〉 j ≥ 0）. It is proved in this paper that （i） if there exists aconstant c≥ 0 such that b（i）-a（i）＋ci is nondecreasing with respect to i and a（i） ＋ u（i） - ci ≥ 0 （i≥ 0）, then VarX（t）-EX（t）≥-X（0）e^-2ct,t≥0, or （ii） if there exists a constant u（i） - c≥ 0 such that b（i）-a（i）＋ci is non-increasing with respect to i and a（i）＋u（i）-ci≤0（i≥0）,then VarX（t） - EX（t） ≤ -X（0）e^-2c,t ≥ 0 Hereb（i） = qii＋1, a（0） = 0, a（i） = ∑j=^ijqii-j （i≥ 1）, u（0） = u（1） =0 and u（i） = 1/2∑j=^ij（j - 1）qii-j （i ≥ 2） . This result covers the results for birth-death processes obtained in [7].     

Привалов定理的拓广

<正> 设Ω是 m 个实变数 u_1,…,u_m 空间中的-p 维可定向流形Ω:(?)Ω称为属于 C~e 类(e是非负的整数),如果实函数 f_1,…,f_(m-p)皆有e次连续偏微商.Ω称为平滑的,如Ω属于 C~1 类并且矩阵     

ON LARGE INCREMENTS OF l~p-VALUED GAUSSIAN PROCESSES

ＯＮＬＡＲＧＥＩＮＣＲＥＭＥＮＴＳＯＦｌｐＶＡＬＵＥＤＧＡＵＳＳＩＡＮＰＲＯＣＥＳＳＥＳＬＩＮＺＨＥＮＧＹＡＮＡｂｓｔｒａｃｔＬｅｔ｛Ｘｋ（ｔ），ｔ≥０｝，ｋ＝１，２，…，ｂｅａｓｅｑｕｅｎｃｅｏｆｉｎｄｅｐｅｎｄｅｎｔＧａｕｓｓｉａｎｐｒｏｃｅ...     

Smooth solution of one boundary-value problem

We study the boundary value problem for the quasilinear equation u _u ? u_xx=F[u, u_t], u(x, 0)= u(x, π)=0, u(x+w, t)=u(x, t), x ε ®, t ε [0, π], and establish conditions under which a theorem on the uniqueness of a smooth solution is true.     

奇异二阶四点边值问题的正解

研究了如下奇异二阶四点边值问题u″(t)+h(t)f(t,u(t))=0,0相似文献   

Transformation Operators in the Problems of Controllability for the Degenerate Wave Equation with Variable Coefficients

Ukrainian Mathematical Journal - We study a control system $$ {w}_{tt}=\frac{1}{\rho }{\left(k{w}_x\right)}_x+\gamma w,w\left(0,t\right)=u(t),x\in \left(0,l\right),t\in \left(0,T\right), $$ in...