具p-Laplacian算子的四阶三点边值问题的迭代解的存在性

研究下列具有p-Laplacian算子的四阶三点边值问题{(φp(u″(t)))″=f(t,u(t),u″(t)),t∈[0,1] u(0)-ξu(1)=0,u′(1)-ηu′(0)=0 u″(0)-a1u″(δ)=0,(φp(u″))′(1)-b1(φp(u″))′(δ)=0其中φp(s)=|s|p-2s,p>1,0<ξ,η<1,0相似文献   

含各阶导数的非线性弹性梁方程的一个存在定理

通过选择适当的Banach空间并利用Leray-Schauder非线性抉择对于含各阶导数的非线性弹性梁方程{u(4)(t)=f(t,u(t),u′(t),u″(t),u′″(t)),0≤t≤1, u(0)=u′(1)=u″(0)=u′″(1)=0.建立了一个解的存在定理．在材料力学中，该方程描述了一端简单支撑，另一端被滑动夹子夹住的弹性梁的形变．这个存在定理说明只要非线性项满足某种线性增长条件该方程至少有一个解．     

Triple positive periodic solutions of nonlinear singular second-order boundary value problems

This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″(t) + λ(t)u(t) = f(t,u(t)),a.e.t ∈ [0,2π],u(0) = u(2π),u′(0) = u′(2π),where f(t,u) is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett–Williams and Krasnosel'skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.     

Maximal regularity of second order delay equations in Banach spaces

We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu't + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2π, 0];X)(resp.Bsp ,q([2π, 0];X) or Fsp,q([-2π, 0;X])).     

具p-Laplace算子的四阶三点边值问题的两个正解

研究下列具有p-Laplace算子的四阶三点边值问题(p(u″(t)))″+a(t)f(u(t))=0,t∈(0,1),u(0)=ξu(1),u′(1)=ηu′(0),(p(u″(0))′=α1(p(u″(δ))′,p(u″(1))=β1(p(u″(δ)),通过利用Avery-Henderson不动点定理,给出了边值问题存在至少两个正解的充分条件.     

一类非线性分数阶微分方程边值问题的正解

讨论以下非线性分数阶边值问题:^cD_(0+)cD_(0+)^αu(t)+λa(t)f(u(t))=0,0cD_(0+)cD_(0+)^α是Caputo导数,λ>0.利用Krasnoselskiis不动点定理,得到其正解存在与不存在的充分条件,最后给出一个例子验证我们的结论.     

一类四阶非线性微分方程两点边值问题的正解

应用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下,获得了一类四阶非线性常微分方程两点边值问题{-u(4)(t)t=f(t,u(t)),≤t≤1,u(0)=u′(0)=u′(1)=u′″(1)=0正解的存在性.     

Three solutions of p-Laplacian equations via a critical point theorem of Ricceri

In this paper,we consider the following quasilinear diferential equation(p(u′))′+λf(t,u)=0subject to one of the two boundary conditions:u(0)=u′(1)=0,u′(0)=u(1)=0.After transforming them into a problem of symmetrical solutions,the existence of three solutions of the problem is obtained by using a recent critical point theorem of Recceri.An example is given to demonstrate our main result.     

OSCILLATION AND ASYMPTOTIC BEHAVIOR OF SOME SECOND-ORDER RETARDED DIFFERENTIAL EQUATIONS

In this paper, we consider the following second order retarded differential equations x″(t)+cx′(t)=qx(t-σ)-lx(t-δ) (1) x″(t)+p(t)x(t-τ)=0 (2) We give some sufficient conditions for the oscillation of all solutions of Eq. (1) in the case where q, ι, σ, δ are positive numbers and c is a real number. And also, we study the asymptotic behavior of the nonoscillatory solutions. If necessary, we give some examples to illustrate our results. At last, we study Eq. (2) with some conditions on p(t).     

一类二阶常微分方程边值问题的无穷多个解

利用变分原理和Z2不变群指标研究了二阶常微分方程边值问题{u″(t)-u(t) f(t,u(t))=0,0＜t＜1,u′(0)=0,α1u(1) u′(1)=0,(其中α1＞-1/2).得出了这类方程存在无穷个解的充分条件.     

Helly’s Principle and Its Application to an Infinite-Horizon Optimal Control Problem

In this paper, a numerical method is presented to solve singularly-perturbed two-point boundary-value problems for second-order ordinary differential equations with a discontinuous source term. First, an asymptotic expansion approximation of the solution of the boundary-value problem is constructed using the basic ideas of the well-known WKB perturbation method. Then, some initial-value problems and terminal-value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial-value problems and terminal-value problems are singularly-perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples are provided to illustrate the method.     

Differential sensitivity of solutions of convex constrained optimal control problems for discrete systems

A family of optimal control problems for discrete systems that depend on a real parameter is considered. The problems are strongly convex and subject to state and control constraints. Some regularity conditions are imposed on the constraints.The control problems are reformulated as mathematical programming problems. It is shown that both the primal and dual optimal variables for these problems are right-differentiable functions of a parameter. The right-derivatives are characterized as solutions to auxiliary quadratic control problems. Conditions of continuous differentiability are discussed, and some estimates of the rate of convergence of the difference quotients to the respective derivatives are given.     

Multiple voting location problems

The facility voting location problems arise from the application of criteria derived from the voting processes concerning the location of facilities. The multiple location problems are those location problems in which the alternative solutions are sets of points. This paper extends previous results and notions on single voting location problems to the location of a set of facility points. The application of linear programming techniques to solve multiple facility voting location problems is analyzed. We propose an algorithm to solve Simpson multiple location problems from which the solution procedures for other problems are derived.     

Apply a novel evolutionary algorithm to the solution of parameter selection problems

In this study, a modified line-up competition algorithm (LCA) is used to solve parameter selection problems. The so-called parameter selection problems contain parameter identification problems and optimal control problems. Once the later problems are transformed by control parametrization, the parameters embedded in both problems are selected by the proposed method under the framework of integration approach. Two parameter identification problems and one optimal control problem are given to demonstrate the use of LCA. The results show that in addition to being insensitive to the initial conditions, LCA is very efficient in solving highly nonlinear parameter selection problems.     

两个反问题的数学模型

本文考察了两个工业中的反问题 ,讨论了如何建立起这些问题的偏微分方程模型 ,并最终归结为变分问题 ,简述了这些模型的求解方法 .     

An asymptotic initial value method for second order singular perturbation problems of convection-diffusion type with a discontinuous source term

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.     

基于服装舒适性的纺织材料设计反问题

纺织材料设计反问题是数学物理反问题的一个新领域,也被称为应用数学与计算数学的一个分支.综述纺织材料设计反问题的来源、数学归结,并基于服装的热湿舒适性、压力舒适性提出了设计反问题,给出了反问题解的定义,综述了求解纺织材料设计反问题的数值算法,列举了若干具有挑战的研究课题.     

A range-space implementation for large quadratic programs with small active sets

Large and sparse convex quadratic programming problems are often generated in the course of solving large-scale optimization problems. An important class of these problems has the property that only a small number of constraints are at their bounds at a solution. We describe an implementation of a range-space method designed for efficient solution of these small-active-set problems. The implementation is oriented toward the application area of multidimensional data fitting subject to constraints. Test results are presented for several data-fitting problems.The authors are indebted to the referees for several valuable contributions     

组合拓扑方法在组合学和图论中的应用

本文介绍组合拓扑方法在图论和组合学中的应用，探索一些新的离散问题和连续问题的关系，介绍目前有关这方面的新结果及发展动向。本文主要介绍同调理论在图论中的应用，与图有关的复形及性质，不动点定理在离散问题中的应用等。文中提出了一些新结果及可供研究的新问题。     

Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions

Mukherjee and Basu proposed a new method for solving fuzzy assignment problems. In this paper, some fuzzy assignment problems and fuzzy travelling salesman problems are chosen which cannot be solved by using the fore-mentioned method. Two new methods are proposed for solving such type of fuzzy assignment problems and fuzzy travelling salesman problems. The fuzzy assignment problems and fuzzy travelling salesman problems which can be solved by using the existing method, can also be solved by using the proposed methods. But, there exist certain fuzzy assignment problems and fuzzy travelling salesman problems which can be solved only by using the proposed methods. To illustrate the proposed methods, a fuzzy assignment problem and a fuzzy travelling salesman problem is solved. The proposed methods are easy to understand and apply to find optimal solution of fuzzy assignment problems and fuzzy travelling salesman problems occurring in real life situations.