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.

EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS

This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.

Sign-Changing Solutions for Discrete Dirichlet Boundary Value Problem

Using invariant sets of descending flow and variational methods, we establish some sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions for second-order nonlinear difference equations with Dirichlet boundary value problem. Some results in the literature are improved.

Fundamental Solution of Dirichlet Boundary Value Problem of Axisymmetric Helmholtz Equation

Fundamental solution of Dirichlet boundary value problem of axisymmetric Helmholtz equation is constructed via modi?ed Bessel function of the second kind, which uni?ed the formulas of fundamental solution of Helmholtz equation, elliptic type Euler-Poisson-Darboux equation and Laplace equation in any dimensional space.

DIRICHLET PROBLEMS FOR STATIONARY VON NEUMANN-LANDAU WAVE EQUATIONS

In this article, we are concerned with the Dirichlet problem of the stationary von Neumann-Landau wave equation：{（-△x＋△y）φ（x,y）=0,x,y∈Ωφ｜δΩxδΩ=fwhere Ω is a bounded domain in R^n. By introducing anti-inner product spaces, we show the existence and uniqueness of the generalized solution for the above Dirichlet problem by functional-analytic methods.

The Criteria for Reducing Centrally Restricted Three-Body Problem to Two-Body Problem

Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius aH and planet mean radius RP and the ratio R1=RP/aH. Under very low R1 (less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R1=RP/aH =0.01 and 5.9862 × 10-3 respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.

POSITIVE CLASSICAL SOLUTIONS OF DIRICHLET PROBLEM FOR THE STEADY RELATIVISTIC HEAT EQUATION

In this paper,for a bounded C2 domain,we prove the existence and uniqueness of positive classical solutions to the Dirichlet problem for the steady relativistic heat equation with a class of restricted positive C2 boundary data.We have a non-existence result,which is the justification for taking into account the restricted boundary data.There is a smooth positive boundary datum that precludes the existence of the positive classical solution.

<i>L^p</i>Polyharmonic Dirichlet Problems in the Upper Half Plane

In this article, a class of Dirichlet problem with Lp boundary data for poly-harmonic function in the upper half plane is mainly investigated. By introducing a sequence of kernel functions called higher order Poisson kernels and a hierarchy of integral operators called higher order Pompeiu operators, we obtain a main result on integral representation solution as well as the uniqueness of the polyharmonic Dirichlet problem under a certain estimate.

Localisation Inverse Problem and Dirichlet-to-Neumann Operator for Absorbing Laplacian Transport

We study Laplacian transport by the Dirichlet-to-Neumann formalism in isotropic media (γ = I). Our main results concern the solution of the localisation inverse problem of absorbing domains and its relative Dirichlet-to-Neumann operator . In this paper, we define explicitly operator , and we show that Green-Ostrogradski theorem is adopted to this type of problem in three dimensional case.

二阶非线性Schr odinger方程Dirichlet问题的整体W^(1,2)解

利用位势井方法研究有界域上二阶非线性Schrdinger方程Dirichlet问题整体解的存在性,得到了位势井深度d=(1/γCγ*)>0,其中:γ=(2(p+1))/(p-1);C*=sup((‖u‖p+1)/‖▽u‖),明确了位势井的形态.通过构造问题近似解得到了近似解的先验估计及相关集合在流之下的不变性,揭示了满足适当条件时在位势井内整体W1,2解的存在性.

平面中Poisson方程的Dirichlet问题

基于向量旋转内积不变的特点,通过对Green积分公式的推广,得到与空间Green三个公式相似的平面Green公式.从而,得到平面中Poisson方程Robin问题的解和平面中Poisson方程Dirichlet问题的解.

随机Poisson方程Dirichlet大地边值问题的随机积分解

利用随机微分方程理论,给出了随机Poisson方程Dirichlet大地边值问题的随机积分解,讨论了随机与确定边值问题间的关联。对应视为随机过程的函数,若采用确定性边值问题求解,不确定性影响将被直接带入最终解中;若采用随机积分解,则类似Gauss白噪声的影响将被滤掉,这对进一步提高重力场的求解精度具有重要影响。

一般区域上Dirichlet-Poisson问题数值解的概率方法

对 2维调和方程第一边值问题曾有人提出了一种高效概率算法 .利用Brown运动进一步对此方法的实质进行了分析 ,并把它推广应用到一类 3维的Dirichlet

Sierpinski Gasket上的布朗运动与Dirichlet问题

利用布朗运动的性质获得了SierpinskiGasket上Dirichlet问题及Neumann问题的解 ,并使解具有更为简捷的表达式 。

S-调和函数与超过程的Dirichlet问题(英文)

本文定义了超Hunt过程的S-调和函数与Dirichlet问题．定义在Dc上的有界函数f可以扩张到Rd上的函数h使得F（P）=exp＜-h。

求解Poisson方程Dirichlet问题的一点补充

求解Poisson方程定解问题通常有分离变量法、积分变换法、格林函数法等重要方法,但传统的求解方法有时运算量较大,求解较麻烦.通过寻求一类特殊的Poisson方程的Dirichlet问题求解方法,即-Δu=f(x)中的f(x)为多项式函数时,Poisson方程的Dirichlet问题可采用比较简单的求解方法,避免了传统求解方法的复杂计算,从而将求解Poisson方程定解问题的方法进一步完善.

重力场Dirichlet问题解的随机Poisson积分表示

在球近似下 ,顾及到庞大复杂的边界数据 ,借助重力场随机模型框架 ,直接给出了调和重力随机场Dirichlet问题解的随机积分表达式———随机Poisson积分式 ,并讨论了这个广义随机泛函与经典Poisson积分表达式的关系。

THE EIGENVALUE PROBLEM FOR THE LAPLACIAN EQUATIONS

This article studies the Dirichlet eigenvalue problem for the Laplacian equations △u = -λu, x ∈Ω , u = 0, x ∈δΩ, where Ω belong to R^n is a smooth bounded convex domain. By using the method of appropriate barrier function combined with the maximum principle, authors obtain a sharp lower bound of the difference of the first two eigenvalues for the Dirichlet eigenvalue problem. This study improves the result of S.T. Yau et al.

THE FIRST BOUNDARY VALUE PROBLEM FOR A CLASS OF QUASILINEAR DEGENERATE ELLIPTIC EQUATIONS

In this paper, the first boundary value problem for quasilinear equation of the form △A（u,x）＋∑i=1^m δb^i（u,x）/δxi＋c（u,x）=0,Au（u,x） ≥0is studied. By using the compensated compactness theory, some results on the existence of weak solution are established. In addition, under certain condition the uniqueness of solution is proved.

S-T-S混合式循环互助教学模式用于少学时“化工原理”课程

“化工原理”课程是化工及相关专业的专业基础课程,相关专业的学时少,课程难,需重点解决的问题是“三多”“三不愿”“三不明”。针对痛点问题,提出了线上线下混合式循环互助的创新设计思路,包括:教师帮助学生自制课前、课中、课后习题,学生帮助教师反馈真实学习情况,学生帮助学生组团互助学习。问卷调查和评教结果显示,在一定程度上解决了“三多”“三不愿”的问题;通过建立“助教团队”反馈不同层次学生的学习情况,较好地解决了“三不明”的问题。学生的成绩与教改前相比有明显提高。