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1.
Let R(t)=u ct-sum from(i=1) to (N(t)) Xi,t≥0 be the renewal risk model,with FX ( x )being the distribution function of the claim amount X. Let ψ (u ) be the ruin probability with initial surplus u. Under the condition of FX (x) ∈ S *(γ ),γ≥ 0,by the geometric sum method,we derive the local asymptotic behavior for ψ (u ,u z for every 0<z<∞. On one hand,the asymptotic behavior of ψ ( u) can be derived from the result obtained. On the other hand,the result of this paper can be applied to the insurance risk management of an insurance company.  相似文献   

2.
It has been observed that for many stable feedback control systems, the introduction of arbitrarily small delays into the loop causes instability. Therefore, robustness of stablility with respect to small delays is of great importance. The authors study the robustness with respect to small delays for exponential stability of Pritchard-Salamon systems with admissible state feedback,i.e. the exponential stability of the following systems are equivalent:{x(t)=S(t)x1 ∫o^tS(t-s)BFx(s)ds u(t)=Fx(t),x0∈V,t≥0and{x(t)=S(t)x0 ∫o^tS(t-s)BFx(s-r)ds u(t)=Fx(t-r),x0∈V,t≥0and obtain a number of necessary and sufficient conditions, particularly, frequency domain characterization for robustness with respect to small delays for exponential stability.  相似文献   

3.
研究了高阶摄动波动方程ttu+(-Δ)mu+V(x)u=0,u(x,0)=0,tu(x,0)=f(x),x∈Rn,n>3m,解的Lp-Lp′估计.在摄动和始值f(x)为紧支且V(x)充分小的假定下,得到了该问题解的Lp-Lp′估计:‖u(*,t)‖p′≤Ct-d‖f‖p,t>0,其中 m>1,d=n/m(1/p-1/p′)-1,1/p+1/p′=1,m/(2n)<1/p-1/2相似文献   

4.
Let q≥5 be a prime number. Let k=Q(√d) be a quadratic number field, where d=(-1)q(q-1)/2. (-(q-1)^q-1UW^q u^2q^q). Then the class number of k is divisible by q for certain integers u,w. Conversely, assume Ω/k is an unramifled cyclic extension of degree q (which implies the class number of k is divisible by q), and Ω2 is the splitting field of some irreducible trinomial f(X)=X^q-aX-b with integer coefficients, k=Q(√D(f)) with D(f) the discriminant of f(X). Then f(X) must be of the form f(X)=X^q-u^q-2 wX-u^q-1 in a certain sense where u,w are certain integers. Therefore, k=Q(√d) with d=(-1)^q(q-1)/2 (-(q-1)^q-1uw^q u^2q^q). Moreover, the above two results are both generalized for certain kinds of general polynomials.  相似文献   

5.
The existence of homoclinic solutions for the second-order p-Laplacian differential system( ρ( t) Φp( u'( t))) '-s( t) Φp( u( t))+ λf( t,u( t)) = 0 with impulsive effects Δ( ρ( tj) Φp( u'( tj))) = Ij( u( tj)) is studied. By using three critical points theorem and variational methods, the sufficient condition is established to guarantee that this p-Laplacian differential system with impulsive effects has at least one nontrivial homoclinic solution. Besides,an example is presented to illustrate the main result in the end of this paper.  相似文献   

6.
The authors obtain some sufficient conditions for the stability of zero solutions to some types of the functional equation. x(t) +p(t)x(t) +q(t)x(t) +f (t, xt) = 0 by transformations and the Liapunov's Second method. The obtained conclusions generalize some results of Stability of Equation x (t) +p( t) x(t) + q(t)x(t) =0 and Jack Hale in his paper of Theory of Functional Differential Equations.  相似文献   

7.
研究下列具有p-Laplacian算子的四阶三点边值问题{(Ψp(u"(t)))"=f(t,u(t),u"(t)),t∈[0,1]u(0)-ξu(1)=0,u"(1)-ηu'(0)=0,u"(0)-αu"(δ)=0,u"(1)-bu(δ)=0,其中ψp(s)=|s|p-2s,p>1,0<ξ,η<1,0<α,b<1,0<δ<1,f∈C([0,1]×R2,R),通过单调迭代方法得到迭代解.  相似文献   

8.
设f满足:H(t)=∫t∞f(dss)<∞,t∈R,∫-∞∞f(dss)=∞(或H(t)=∫t∞f(dss)<∞,t>0,∫0∞f(dss)=∞,且f'(t)∫t∞f(dss)在R(或(0,∞))上有界,构造爆炸上解和爆炸下解,得到了非线性椭圆型问题Δu=f(u),x∈Ω,u|Ω= ∞解的存在性和渐近行为的全局最优估计.  相似文献   

9.
1. Let X and Y be two sets of points on each of which a completely additive measure is given. Let K(x,y,u) be a real-valued function which is defined for every pair of points (x,y) ∈ (X,Y) and for every real number u, such that, for almost every point x∈X it satisfies the Caratheodory condition with respect to (y,u): K(x,y,u) is measurable in y for every u and continuous in u for almost every y. For every measurable function f(y), the functionKxf(y) = K(x,y,f(y))is measurable in y for almost every x. If this funetion is integrable with respect to y for almost every x, the value of the integral yields a function Kf:defined for almost every a∈ X. We call the functional operator K the operator generated by the function K(x,y,u).  相似文献   

10.
p-Benzoquinone (BQ) is a promising candidate for next-generation sodium-ion batteries (SIBs) because of its high theoretical specific capacity, good reaction reversibility, and high resource availability. However, practical application of BQ faces many challenges, such as a low discharge plateau (~2.7 V) as cathode material or a high discharge plateau as anode material compared with inorganic materials for SIBs and high solubility in organic electrolytes, resulting in low power and energy densities. Here, tetrahydroxybenzoquinone tetrasodium salt (Na4C6O6) is synthesized through a simple neutralization reaction at low temperatures. The four –ONa electron-donating groups introduced on the structure of BQ greatly lower the discharge plateau by over 1.4 V from ~2.70 V to ~1.26 V, which can change BQ from cathode to anode material for SIBs. At the same time, the addition of four –ONa hydrophilic groups inhibits the dissolution of BQ in the organic electrolyte to a certain extent. As a result, Na4C6O6 as the anode displays a moderate discharge capacity and cycling performance at an average work voltage of ~1.26 V versus Na/Na+. When evaluated as a Na-ion full cell (NIFC), a Na3V2(PO4)3 || Na4C6O6 NIFC reveals a moderate discharge capacity and an average discharge plateau of ~1.4 V. This research offers a new molecular structure design strategy for reducing the discharge plateau and simultaneously restraining the dissolution of organic electrode materials.  相似文献   

11.
本文阐述了以下二阶拟线性微分方程的解的振荡性,有界性和单调性的一些新结果。(p(t)(y’(t))α)’=q(t)yβ(t) r(t),t≥tο其中,tο是非负实数,当t≥tο时,p(t)是连续的正实函数,r(t)是连续的实函数,q(t)是非负的连续的实函数且q(t)≠0,α和β都是正奇整数的商数。  相似文献   

12.
The distribution of zeros of solutions of the advanced differential equations with an advanced variable x′(t)-P(t)x(τ(t))=0,t≥t0 is studied, where P(t)∈C([t0,∞),R^+),τ:[t0,∞)→R^+ are continuously differentiable and strictly increasing,τ(t)≥t and limt→∞τ(t)=∞.The estimate for the distance between adjacent zeros of the oscillatory solution of the above equation is obtained.  相似文献   

13.
由强迫函数诱导的高阶泛函微分不等式的有界振动   总被引:1,自引:0,他引:1  
本文考虑了非线性泛函微分不等式X(t){LnX(t)十f(t,x(g1(t))),…X(gm(t)))-h(t)}≤0.(当n为奇数时)(1)x(t){Lnx(t)-f(t,x(g1(t)),…X(gm(t)}≥0(当n为偶数时)(2)的振动问题,得到了不等式(1)和(2)的一切有界解振动和一切解振动的充分条件.  相似文献   

14.
采用重合度理论中的延拓定理, 研究一类三阶p-Laplacian中立型方程:(φp((x(t)-cx(t-σ))″))′+f1(x(t))x′(t)+f2(x′(t))x″(t)+ρ(t)g(x(t-τ(t)))=e(t)T-周期解的存在性, 得到了该方程存在T-周期解的相关结果.  相似文献   

15.
考虑以下三阶三点边值问题:u''(t)+a(t)f(u(t))=0,t∈(0,1);u(0)=u″(0)=0,u'(1)-αu(η)=λ,其中0η1,0α1/η,λ∈(0,∞),通过建立相关线性边值问题的格林函数得到解的形式,运用不动点指数理论建立了上述边值问题至少两个正解的存在性准则.  相似文献   

16.
Some new sufficient conditions for the oscillation of the neutral equation d/dt[y(t)-R(t)y(t-r)]+P(t)y(t-τ)-Q(t)y(t-σ)=0,where P, Q, R∈C([t0,∞), R^+) and r, τ,σ∈(0,∞),are obtained for the case where former results can not be applied in this paper.  相似文献   

17.
固体推进剂粘弹泊松比的研究   总被引:4,自引:0,他引:4  
  相似文献   

18.
考虑如下周期系统x(′t)=A(t)x(t+t∫-∞C(t,s)x(s)ds+∫t-∞D(t,s)x(′s)ds+b(t)利用指数型二分性及压缩不动点定理,解决了其周期解的存在性问题,给出其周期解存在的充分性条件,将原有的一维标量方程的结论推广到n维情形.  相似文献   

19.
一类二阶非线性泛函微分方程的渐近稳定性   总被引:1,自引:0,他引:1  
利用Lyapunov泛函方法 ,讨论了一类二阶非线性泛函微分方程x″(t) +φ(x′(t) ,t) +f(x(t-r(t) ) ) =0解的渐近稳定性 ,基于|x′(t) |积分的下半有界性 ,得到关于x′(t)的主要引理 ,改进了 φ(x′(t) ,t) /x′(t)积分上界、下界的条件 ,得到了一些新结果 ,推广了方程在线性、非线性、常时滞、变时滞情形下某些相关结论  相似文献   

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