POSITIVE SOLUTIONS FOR SINGULAR BVPs ON THE POSITIVE HALF-LINE ARISING FROM EPIDEMIOLOGY AND COMBUSTION THEORY

In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi- demiology and combustion theory set on the positive half-line are investigated upper and lower solution techniques combined with fixed point index on cones in priate Banach spaces. The results complement recent ones in the literature. We use appropriate Banach spaces. The results complement recent ones in the literature.

EXISTENCE RESULTS FOR DEGENERATE ELLIPTIC EQUATIONS WITH CRITICAL CONE SOBOLEV EXPONENTS

In this paper, we study the existence result for degenerate elliptic equations with singular potential and critical cone sobolev exponents on singular manifolds. With the help of the variational method and the theory of genus, we obtain several results under different conditions.

POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER SINGULAR NONLINEAR DIFFERENTIAL EQUATIONS

New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the conditions 0 less than or equal to f(0)(+) < M-1, m(1) < f(infinity)(-)less than or equal to infinity or 0 less than or equal to f(infinity)(+)< M-1, m(1) < f (-)(0)less than or equal to infinity where f(0)(+) = lim(u -->0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory.

MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS TO SECOND ORDER SINGULAR DIFFERENTIAL SYSTEMS

In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray- Schauder type and Krasnoselskii fixed point theorem in cones.

RADIAL CONVEX SOLUTIONS OF A SINGULAR DIRICHLET PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE

In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theorem in cones. We deal with more general nonlinear term than those in the literature.

MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE

In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

Positive Solution for a Singular Fourth-Order Differential System

In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system u(4) = φu + f (t, u, u”, φ), 0 < t < 1, -φ” = μg (t, u, u”), 0 < t < 1, u (0) = u (1) = u”(0) = u”(1) = 0, φ (0) = φ (1) = 0;where μ > 0 is a constant, and the nonlinear terms f, g may be singular with respect to both the time and space variables. The results obtained herein generalize and improve some known results including singular and non-singular cases.

一维p-Laplacian方程多解的存在性

利用Leggett-Milliams定理,建立了一类一维奇异p-Laplacian非线性边值问题((u″))″+a(t)f(u)=0,u(0)=u(1)=u″(0)=u″(1)=0三解的存在性定理,其中(s)=|s|p-2s,p>1,推广并丰富了以往文献的一些结论.

奇异非线性四阶边值问题的正解

证明存在两个正数 0 <λ <λ <+∞ ,使得奇异非线性四阶边值问题y( 4 ) (x) =λh(x)f(y(x) ) , 0 <x <1 ,y( 0 ) =y( 1 ) =y′( 0 ) =y′( 1 ) =0 ,当λ∈ ( 0 ,λ )时 ,无正解 ;当λ∈ (λ ,+∞ )时 ,存在 1个正解 ;当λ∈ (λ ,+∞ )时 ,存在 3个解 ,其中有 2个为正解 ,只要f(y)在y =0处是超线性 ,并在y

p-Laplacian算子型奇异边值问题的正解

运用锥拉伸压缩原理,讨论了一类具有p- Laplacian算子型的非线性奇异边值问题正解的存在性,并对所得结果给出了一些应用和例子.

异形牙轮单牙轮钻头的计算机仿真模型研究

讨论了一种新型单牙轮钻头——异形牙轮单牙轮钻头。在钻头几何学和运动学的基础上,通过坐标变换方法实现了钻头上各牙齿的空间位置变换,建立了随钻运动的单牙轮钻头的计算机仿真模型。仿真模型可模拟钻头钻进过程中牙轮上各牙齿的形状、大小、钻头上各牙齿的布置及钻头钻进过程中各牙齿间的相互位置关系,是钻头与岩石相互作用仿真研究的核心问题,也是分析研究单牙轮钻头工作行为的基础。

二阶奇异微分方程边值问题正解的存在性

该文通过构造一个特殊的锥,利用锥压缩与锥拉伸不动点定理,研究了一类二阶奇异微分方程边值问题两个正解的存在性,改进了最近的一些结果.

非线性奇异三点边值问题正解的存在性

研究非线性奇异三点边值问题正解的存在性.首先将边值问题转化为相应的算子方程,然后根据Kransnosel'skii不动点定理得出算子方程不动点的存在性,从而给出边值问题正解存在的充分条件.

一类二阶奇异半正边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸不动点定理,研究了一类二阶奇异半正Sturm-liouville边值问题,得到了其C1p[0,1]正解存在的一个判定方法.

三阶奇异边值问题的多解性

利用锥上的不动点定理和Green函数的性质,本文在较弱条件下研究了三阶奇异非线性边值问题的多个正解的存在性。

奇异二阶微分系统边值问题

运用锥拉伸与锥压缩原理,在适当的条件下建立一类奇异二阶微分系统边值问题正解的存在性。突破了有关文献中要求非线性项超线性或次线性增长的限制。

奇异边值问题的正解

利用锥拉伸与压缩不动点定理研究了一类带特征值的奇异边值问题,得到了正解的存在性及个数。

橡胶类材料与刚性锥之间的大变形接触问题

应用大变形理论对刚性锥压缩作用下橡胶类材料半空间锥尖附近的应力奇异场进行了分析．研究揭示，奇异场由两个区构成；分别为扩张区（ＥＳ）和收缩区（ ＳＳ）．同时给出了两个区的基本方程、应力奇异性及应力随角坐标的变化曲线．

二阶奇异非线性微分方程边值问题的正解

分别在0≤f+0 <M1,m1<f- ∞ ≤∞和 0 ≤f+∞ <M1,m1<f- 0 ≤∞的情形下研究了非线性奇异边值问题u″+g(t)f(u) =0 ,0 <t <1,αu( 0 ) - βu′( 0 ) =0 ,γu( 1) +δu′( 1) =0 正解的存在性 ,其中f +0 =limu→ 0 f(u) /u ,f- ∞ =limu→∞f(u) /u ,f- 0 =limu→ 0 f(u) /u ,f +∞=limu→∞f(u) /u ,g在区间 [0 。

基于奇异摄动的捷联惯导伪圆锥误差补偿算法

提出了一种新的高精度捷联惯导系统（SINS）姿态更新算法——基于奇异摄动理论的算法。该方法是对伪圆锥误差较大的传统Savage姿态更新算法改进，它运用奇异摄动理论抑制载体真实的角运动频率与宽频带噪声的频率混叠在一起时出现的圆锥误差放大现象——伪圆锥误差，同时将陀螺输出分为快变部分和慢变部分，利用陀螺敏感的载体角运动与陀螺非理想输出信号的两时间尺度特性补偿伪圆锥误差。该算法通过可调参数以控制任意频段的伪圆锥误差的影响，实现算法精度的提高。仿真结果表明，此新方法与目前高精度的Savage四子样算法相比不仅能够提高姿态更新的精度和速率，而且具有良好的灵活性和较小的计算量。