一类含临界指数的Schr?dinger-Poisson系统的多重正解的存在性

本文研究一类含临界指数的Schr?dinger-Poisson系统的多重正解的存在性问题,利用变分方法,建立了多重正解的存在性,获得了至少存在两个正解的结果.     

奇异边值问题的正解存在性

该文应用不动点定理,研究了非线性二阶奇异边值问题正解的存在性和多个正解存在性,改进和推广了近期文献［６］的结果．     

分歧和一类p-Laplace问题的正解（英文）

本文研究一类在零点或无穷远点非渐近线性的p-Laplace问题.利用分歧和拓扑方法,获得了问题正解的存在性,不存在性和多解性结果,丰富和推广了正解存在性的已有结果.     

二阶非线性中立型时滞差分方程的正解

本文研究了一类二阶非线性中立型时滞差分方程的正解,得到了最终正解的存在性判据及存在正解的必要条件,建立了一些正解不存在性定理,所得结论推广并改进了已知的一些结果。     

带Riemann-Stieltjes积分条件的三阶边值问题的单调正解

研究了一类带Riemann-Stieltjes积分条件的非线性三阶非局部边值问题,将边值问题正解存在性的研究转化为扰动Hammerstein积分方程的研究,通过构造Green(格林)函数及讨论其性质,运用推广的Leggett-Williams型不动点定理,得到了至少存在3个和2n-1个正解的存在性准则, 所得结果推广和改进了最近文献中的结果,并充分反映了非线性项含导数对正解存在性研究的影响.主要结果由实例加以阐述.     

共振情形下一类非合作反应堆数学模型正解的存在性

研究一类源自核反应堆的二阶非合作微分系统正解的存在性,其中非线性项为变号函数.运用分歧理论为该系统建立了数个正解的存在性结果,并得到保证正解存在的最优充分条件.所得结果丰富并补充了已有文献的相关结论.     

四阶奇异边值问题的正解

研究了一类四阶奇异边值问题正解的存在性,在f和g满足比超线性和次线性条件更广泛的极限条件下,利用锥压缩和拉伸不动点定理获得了正解的存在性结果,推广和包含了一些已知结果.     

Banach空间高阶周期边值问题正解的存在性

本文研究了Banach空间E中的高阶周期边值问题正解的存在性.利用非紧性测度的估计技巧与凝聚映射的不动点指数理论,获得了该问题正解的存在性结果,推广了某些已有的相应结果.     

一类高阶分数阶微分方程组多点边值问题的多解性

对于一类高阶分数阶微分方程组多点边值问题,借助于Leggett-Williams不动点定理和Leray-Schauder不动点定理研究了该问题至少有三个正解及任意奇数个正解的存在性,所得结果推广了已有文献的存在性结果,并举例验证主要结果.     

一类四阶差分方程多点边值问题的正解

为解决多点支撑弹性梁的正解的存在性问题,运用锥上不动点指数理论,研究一类含参四阶差分方程多点边值问题.获得了当参数在一定范围内取值时正解的存在性结果,得到了正解存在的充分条件.     

Boundary Value Problems with Compatible Boundary Conditions

If Y is a subset of the space ℝⁿ × ℝⁿ, we call a pair of continuous functions U, V Y-compatible, if they map the space ℝⁿ into itself and satisfy Ux · Vy ≥ 0, for all (x, y) ∈ Y with x · y ≥ 0. (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary differential n-dimensional system is investigated, provided the boundary conditions are given via a pair of compatible mappings. By using a truncation of the initial equation and restrictions of its domain, Brouwer's fixed point theorem is applied to the composition of the consequent mapping with some projections and a one-parameter family of fixed points P _δ is obtained. Then passing to the limits as δ tends to zero the so-obtained accumulation points are solutions of the problem.     

奇异边值问题的边界非正则正解

本文讨论一类二阶奇异边值问题正解的存在性．证明了这类问题存在边界非正则正解．     

Boundary Estimates for Solutions of the Parabolic Free Boundary Problem

Let u and solve the problem

Asymptotic Boundary Value Problem of Harmonic Maps via Harmonic Boundary

We prove that given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a ball in the normal range, there exists a harmonic map from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f.     

Three-Dimensional Boundary Value Problems of Elastothermodiffusion with Mixed Boundary Conditions

We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [1–8], we prove theorems on the existence and uniqueness of the classical solutions of these problems.     

Boundary Layers and Boundary Hinge-Support Conditions for Thin Plates

The boundary-layer phenomenon is investigated for a thin three-dimensional plate. An arbitrary anisotropy of elastic properties and nonhomogeneity in longitudinal and transversal directions are assumed. Several initial asymptotic terms are constructed and a way of continuing the asymptotic procedure is described. Precise estimates of the difference between the exact and approximate solutions are obtained for the energy norm. An amalgamated problem is formed that gives the two-term asymptotics of the fields of displacements and stresses at a distance from the lateral side of the plate, whereas the edge effects are simulated by conditions of elastic fastening containing integral characteristics of the boundary-layer problem in the semistrip. Hinge-support conditions due to a sufficiently narrow clamped zone at the edge of the plate are derived and justified as well. Bibliography: 48 titles.     

边界条件带导数的积分边值问题的正解

研究如下二阶积分边值问题的正解:■其中f∈C([0,1]×R~+,R~+).在先验估计的基础上,利用不动点指数理论建立了正解的存在性和多重正解的存在性.     

非特征边界的MHD方程的边界层

考查了小粘性时非特征边界情况下MHD方程在边界附近的性质,说明速度在边界上不为零.源于之前非特征边界条件下不可压缩Navier-Stokes方程边界层的工作,证明了边界层的存在性,并得到了当粘性收敛于零时,MHD方程的解收敛于理想MHD方程的解.     

From the Boundary of the Convex Core to the Conformal Boundary

If N is a hyperbolic 3-manifold with finitely generated fundamental group, then the nearest point retraction is a proper homotopy equivalence from the conformal boundary of N to the boundary of the convex core of N. We show that the nearest point retraction is Lipschitz and has a Lipschitz homotopy inverse and that one may bound the Lipschitz constants in terms of the length of the shortest compressible curve on the conformal boundary.     

具有非线性边界条件的向量边值问题的奇摄动

该文利用微分不等式理论证明了具有非线性边界条件的非线性系统摄动解的存在，并给出了解的按分量直到O（εN 1）的一致有效的估计．