测度链上P-Laplacian算子的Sturm-Liouville边值问题的正解

利用锥上的不动点定理,研究了测度链上四阶p-Laplacian Sturm-Liouville边值问题■正解的存在性,得到了至少存在两个正解的充分条件.这里p1且f:[f:(ρ(a),b]×R~+→R~+(R~+:=[0,∞))连续.     

非线性奇异Hammerstein积分方程的正解

利用锥压缩和锥拉伸不动点定理研究下列非线性奇异Hammerstein积分方程正解及多重正解的存在性u(t)=∫_0~1k(t,s)a(s)f(s,u(s))ds其中f∈C([0,1]×R~+,R~+),a∈L(0,1),a在[0,1]上可奇异且非负,满足∫_0~1a(t)dt0, k∈C([0,1]×[0,1],R~+).非线性项f的超线性和次线性增长条件都是用线性积分算子的第一特征值刻画的,从而本质推广了和改进了现有文献的结果.作为应用,还讨论了一个二阶奇异Sturm-Liouville问题的正解及多重正解的存在性问题.     

非线性边值问题正解存在性的特征值判据

讨论了二阶常微分方程边值问题{-u~n(t)=f(t,u(t)),t∈[0,1],u(0)=u(1)=0正解的存在性,其中f:[0,1]×R~+→R~+连续.给出了该问题存在正解的新特征值判据,该判据改进了以前文献中的相关结果.我们的论证基于锥上的不动点指数理论.     

一类边界条件中带有扰动参数的积分边值问题正解的存在性

本文研究边界条件中带有扰动参数的积分边值问题正解的存在性与不存在性及扰动参数对正解存在性的影响.利用不动点指数理论,得出边值问题至少有一个正解、两个正解以及无解的充分条件.     

拟线性Schrdinger-Poisson方程正解、负解、变号解的存在性

本文考虑拟线性Schrdinger-Poisson方程{-△u+V(x)u+Φu-1/2△(u~2)u=f(x,u),x∈R~3,-△Φ=u~2,x∈R~3,其中f是一个C~1超线性且次临界的非线性项,V是正的有界位势.利用扰动方法,我们证明了该方程非平凡解、正解、负解、变号解的存在性.     

全空间上一类非齐次椭圆方程正解的衰减

本文研究了非齐次椭圆方程不同衰减正解的存在性和衰减问题.利用上下解方法,得到了两个有着不同衰减的正解的存在性,推广了文献[2]中非齐次方程正解的存在性.     

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。     

带有积分边界条件的非线性四阶奇异微分方程组的正解

通过构造一个特殊的锥,并在锥上应用不动点定理,得到了具有积分边界条件的四阶奇异微分方程组单个正解、多个正解的存在性和方程组正解的不存在性.     

一类具有扩散的捕食-食饵模型正解的存在性和惟一性

考虑了一类带Beddington-DeAngelis反应项的捕食-食饵模型正解的存在性和惟一性. 首先利用分歧理论给出正解存在的充分条件, 并刻画了整体分歧的结构. 然后利用特征值变分原理将所给的条件简化, 从而得到正解存在的更为简单更好计算的充分条件和必要条件. 最后利用隐函数定理和广义极大值原理在一维情况下给出了正解的存在惟一性.     

一类奇异次线性边值问题正解存在的充分必要条件

本文研究一类奇异次线性边值问题正解的存在性，得到Ｃ［０，１］正解和Ｃ１［０，１］正解存在的充分必要条件，也得到正解的唯一性．     

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.     

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.     

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.     

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 Estimates for Solutions of the Parabolic Free Boundary Problem

Let u and solve 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．     

SLE Boundary Visits

We study the probabilities with which chordal Schramm–Loewner evolutions (SLE) visit small neighborhoods of boundary points. We find formulas for general chordal SLE boundary visiting probability amplitudes, also known as SLE boundary zig-zags or order refined SLE multi-point Green’s functions on the boundary. Remarkably, an exact answer can be found to this important SLE question for an arbitrarily large number of marked points. The main technique employed is a spin chain–Coulomb gas correspondence between tensor product representations of a quantum group and functions given by Dotsenko–Fateev type integrals. We show how to express these integral formulas in terms of regularized real integrals, and we discuss their numerical evaluation. The results are universal in the sense that apart from an overall multiplicative constant the same formula gives the amplitude for many different formulations of the SLE boundary visit problem. The formula also applies to renormalized boundary visit probabilities for interfaces in critical lattice models of statistical mechanics: we compare the results with numerical simulations of percolation, loop-erased random walk, and Fortuin–Kasteleyn random cluster models at Q = 2 and Q = 3, and find good agreement.     

Boundary in context

A contextualist account of modal assertions is sketched that makes their truth sensitive to the presuppositions of the conversation. Support for the account is mustered by considering its application to the context-sensitivity of assertions of subjunctive conditional sentences, explanation sentences, and knowledge sentences.