一类三阶拟线性方程两点边值问题的奇摄动

本文借助不动点原理,对一类三阶拟线性方程的边值问题的渐近解作了估计,得到了包括边界层在内的任意次近似的一致有效的渐近展开式。     

Existence of periodic solutions of higher order nonlinear functional difference equations

Sufficient conditions for the existence of at least one periodic solution of two classes of functional difference equations are established, respectively.     

无限区间上多分数阶微分方程初值问题解的存在与唯一性

本文研究一类无限区间上具有Riemann-Liouville 导数的多分数阶非线性微分方程初值问题,在一类加权函数空间上使用Schauder 不动点定理建立了该问题解的存在性和唯一性结果, 举例说明了定理的应用.     

SEMIPOSITONE PROBLEM FOR THE nTH-ORDER DELAYED DIFFERENTIAL SYSTEM

In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the corresponding result on the second order de-layed differential equation. Our proofs are based on the well-known Guo-Krasnoselskii fixed-point theorem.     

Generalized variational principles with several arbitrary parameters and the variable substitution and multiplier method

The functional transformations of variational principles in elasticity are classified as three patterns: Ⅰ relaxation pattern, Ⅱ augmented pattern and III equivalent pattern.On the basis of pattern Ⅲ, the generalized variational principles with several arbitrary parameters are formulated and their functionals are defined. They are: the generalized principle of single variable u with several parameters, the generalized principle of two variables u, σ with several parameters, the generalized principle of two variables u, ε with several parameters, and the generalized principle of three veriables u, ε, σ with several parameters. From these principles, a series of new forms of equivalent functionals can be obtained. When the values of these parameters are properly chosen, a series of finite element models can be formulated.In this paper, the question of losing effectiveness for Lagrange multiplier method is also discussed. In order to "recover" effectiveness for multiplier method, a modified method, namely, the variable substitution and multiplier method, is proposed.     

On Implicit Vector Variational Inequalities

In this paper, we study the existence of solutions of implicit vector variational inequalities for multifunctions. Generalized pseudomonotonicity concepts are introduced. Our results extend and unify corresponding earlier existence results of many authors for vector variational inequalities under the Hausdorff topological vector space setting.     

Existence of solutions for parabolic type evolution differential inclusions and the property of the solution set

IntroductionInrecenttenyears,becauseoftheneedofthecontroltheoryandeconomics,thetheoryofdifferentialinclusionshasbeendevelopingfast,andsome~tresultSindifferenhalinclusionshavebeenobtained.Asystematicstudyondifferenhalinclusionscanbefoundin[l].Inordertosuitcontroltheory,thefollowingsendlineardifferentialinclusionswereconsideredin[2~4]:x'(t) Ax(t)6F(t,x(t)),a.e.teI,x(0)=xo'(l)xthereAgeneratesalinearsendgroup(compactorequicolltinuouS),XisasepotleBanachspaCe,I=[0,TiisanintervalofR,F:IxX~Zx\0i…     

用改进的凝聚约束同伦方法求解一类Brouwer不动点问题

In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65), the main adavantages of this method are as follows: on the one hand, it can solve the Brouwer fixed-point problems in a broader class of nonconvex subsets Ω in Rn (in this paper, we let Ω = [x ∈ Rn: gi(x) ≤ 0, i = 1,… ,m]); on the other hand, it can also deal with the subsets Ω with larger amount of constraints more effectively.     

p-Laplace方程混合边值问题正解的存在性

运用锥上的不动点理论，讨论了p—Laplace方程混合边值问题正解的存在性。