EXISTENCE OF SIGN-CHANGING SOLUTION FOR THREE-POINT BOUNDARY VALUE PROBLEM

In this paper,by using the fixed-point index theory,we study the existence of sign-changing solution to some three-point boundary value problem {y″(t) f(y)=0,t∈[0,1], y(0)=0,y′(1)=αy′(η), where 0<α<1,0<η<1,f:R→R is continuous,strictly increasing and f(0)=0.     

一类四阶常微分方程两点边值问题解的存在唯一性

利用压缩映射原理讨论了边值问题y(4)(t)=f(t,y,y′,y,″y′″),y(a)=y(b)=0,y″(a)=y″(b)=0解的存在唯一性问题,得出了当f满足Lipschitz条件时边值问题解的存在唯一性定理,并证明了当f为半线性f(t,y)时结论是最优的.同时给出了一个改进的Picard迭代误差公式,此公式保证了端点处误差为零.     

曲线与其曲率圆

设一条曲线的方程为y=f(x).该曲线在点M(x_0,y_0)处的曲率圆在切点附近的一支曲线方程设为y=g(x),并设f(x)在x=x_0附近有三阶连续导数,且f″(x_0)≠0.将f(x)-g(x)在x=x_0处展开为二阶泰勒公式(注意到 f(x_0)=g(x_0),f′(x_0)=g′(x_0)及f″(x_o)=g″(x_0):     

一类四阶两点边值问题正解的存在性

运用上下解方法及拓扑度理论讨论了非齐次边界条件下四阶两点边值问题u″″(t)=f(u(t)),t∈(0,1),u(0)=u″(0)=u″(1)=0,u(1)=λ,其中λ＞0为参数,f∈C([0,+∞),[0,+∞)).在非线性项满足一定的增长条件下,获得了上述问题存在正解时λ的取值范围.     

非线性特征值问题正解的存在性

证明了四阶边值问题y(4) =λα( x) f ( y( x) ) ,　 0 0且充分小时正解的存在性 .其中 ,α:[0 ,1 ]→ R连续 ,f ( 0 ) >0 .本文的工具是L eray- Schauder不动点定理 [4] .     

一类非线性四阶问题正解的存在性和多解性(英文）

本文研究非线性四阶问题u~″″(t)=λh(t)f(u(t)),t∈(0,1),u(0)=u(1)=u″(0)=u″(1)=0,正解的存在性和多解性,其中λ0,h:[0,1]→(0,∞)连续,f:R→[0,∞)连续.主要工具为Dancer全局分歧定理.     

四阶微分方程共振问题解的多重存在性

利用Z_2-指标理论和临界点理论,讨论了一类四阶微分方程u~((4))+au″=μu+y(t,u),0tL,u(0)=u(L)=u″(0)=u″(L)=0共振问题解的多重存在性,这里00,f∈C~1([0,L]×R,R),为特征值问题u~((4))+au″=λu的某个特征值,其中特征值满足λ_40,λ_k0,k≥2.     

Carathéodory条件下三阶半正边值问题的正解

不要求非线性项f(t,u)连续且下方有界,在f(t,u)满足Carathéodory条件下,讨论了三阶半正边值问题u+λf(t,u)=0,0t1,u(0)=u′(0)=u″(1)=0.当λ>0且充分小时正解的存在性,应用的工具为锥上的不动点.     

四阶微分方程的迭代解

利用一个构造性的方法,在假设边值问题存在上解α和下解β,满足β≤α的前提下,给出了两个单调序列它们一致收敛于如下两类边值问题的极值解u(4)(x)-Mu″(x)=f(x,u(x),u'(x),u″(x),u″'(x)),0＜x＜1,u(0)=u'(1)=u″(0)=u″'(1)=0;u(4)(x)-Mu″(x)=g(x,u(x),u'(x),u″(x)),0＜x＜1,u(0)=u'(1)=u″(0)=u″'(1)=0.     

n阶泛函微分方程边值问题

本文研究下列n阶RFDE边值问题:x⁽ⁿ⁾(t)=f(t,x_t,x(t),x′(t),…,x^(n-1)(t)),　t∈［0,T ］,x(t)=φ(t),t∈［-r,0］;x′(0)=η,x″(0)=η₂,…,x^(n-2) (0)=η_n-2,x^(j)(T)=A,其中j∈I={0,1,2,…,n-1},得到了解的存在性和唯一性新的结果.     

一类具有抑制剂的非均匀恒化器模型的共存态

研究了一类具有抑制剂和Beddington-DeAngelis功能反应项的非均匀恒化器模型.根据单调动力系统理论得到了正平衡解的存在性.利用度理论、分歧理论以及摄动理论,分析了抑制剂对系统正平衡解及渐近行为的影响.结果表明当体现抑制作用的参数μ充分大时,此模型或者没有正解,并且一个半平凡晌非负解是全局吸引的;或者模型的所有正解均由一个极限问题决定.     

Two inequalities with an application

Summary An inequality used in Brown and Cohen (1974,Ann. Statist., 2(5), 963–976) and Bhattacharya (1978,Ann. Inst. Statist. Math., A,30, 407–414) is generalized and another useful inequality derived from it. An application of the latter which provides a more elegant approach to and an improvement over a result in Shinozaki (1978,Commun. Statist. Theor. Meth., A,7, 1421–1432), is also presented.     

Optimization with an approximate Lagrangian

An error analysis is provided for discrete Lagrangian cell problems where the exact objective function for each cell is approximated by a simpler expression. Easily-calculated rigorous and heuristic bounds are given for the error in the value of the objective function. The solution itself, however, can be significantly distorted.     

Auctions with an asking price

This paper studies a sales mechanism, prevalent in housing markets, where the seller does not reveal or commit to a reserve price but instead publicly announces an asking price. We show that the seller sets an asking price such that, in equilibrium, buyers of certain types would accept it with positive probability. We also show that this sales mechanism, with an optimally chosen asking price set prior to the seller learning her value, does better than any standard auction with a reserve price equal to the seller’s reservation value. We then extend the analysis to the case where the asking price reveals information about the seller’s reservation value. We show that in this case there is a separating equilibrium with fully-revealing asking prices, which is revenue-equivalent to a standard auction with a reserve price set at the seller’s reservation value.     

Stretching of an Elastoplastic Plate with an Arbitrarily Oriented Crack

The problem of determination of the crack resistance of an elastoplastic plate, weakened by a rectilinear slit in the form of a cut, under the conditions of uniaxial stretching is considered. The material of the body is assumed to be incompressible, reinforcing, and obeying the Mises condition of plasticity. The straining theory of plasticity is used. The solutions are obtained in the elastic and plastic regions in the form of asymptotic expansions in the neighborhood of the end of the crack. Based on the conditions that the crack borders are unloaded and the elastic and plastic solutions are conjugate on the contour of the plastic region, unknown constants of integration are found. The two-leafed contours of the plastic region are obtained. The critical load is determined.     

Cyclic Extension of an Elastic Fibre with an Elastic-plastic Coating

A circular cylindrical elastic fibre has a concentric coatingof elastic-plastic material which obeys Tresca's yield conditionand associated flow rule. Theoretical solutions are given forthe uniform extension of the composite cylinder; both infinitesimaland finite extensions are considered. The unloading and subsequentreloading of the cylinder are also analysed. The problem isof interest in connection with the mechanics of fibre-reinforcedmetals. Numerical results are given for an aluminium-silicasystem. Good qualitative agreement with experiment is obtained.