POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER SINGULAR NONLINEAR DIFFERENTIAL EQUATIONS

New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the conditions 0 less than or equal to f(0)(+) < M-1, m(1) < f(infinity)(-)less than or equal to infinity or 0 less than or equal to f(infinity)(+)< M-1, m(1) < f (-)(0)less than or equal to infinity where f(0)(+) = lim(u -->0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory.

Positive Solutions for a Class of Second-order m-point Boundary Value Problems

Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive solutions are obtained. The associated Green function of this problem is also given.

ON SOME BOUNDARY VALUE PROBLEMS FOR NONHOMOGENOUS POLYHARMONIC EQUATION WITH BOUNDARY OPERATORS OF FRACTIONAL ORDER

In the paper we study questions about solvability of some boundary value prob- lems for a non-homogenous poly-harmonic equation. As a boundary operator we consider differentiation operator of fractional order in Miller-Ross sense. The considered problem is a generalization of well-known Dirichlet and Neumann problems.

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.

Positive Solutions for Singular Boundary Value Problems of Coupled Systems of Nonlinear Differential Equations

We establish the existence of positive solutions for singular boundary value problems of coupled systems? The proof relies on Schauder’s fixed point theorem. Some recent results in the literature are generalized and improved.

ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR THE POISSON EQUATION WITH A NONLOCAL BOUNDARY OPERATOR

In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order.

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.

Existence of Positive Solutions for Singular Second-order m-Point Boundary Value Problems

The singular second-order m-point boundary value problem , is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (Lϕ)(x) = (p(x)ϕ′(x))′ + q(x)ϕ(x) and ξ i ∈ (0, 1) with 0 【 ξ1 【 ξ2 【 · · · 【 ξ m−2 【 1, a i ∈ [0, ∞). h(x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions is obtained by means of fixed point index theory. Similar conclusions hold for some other m-point boundary value conditions.

TWIN POSITIVE SOLUTIONS TO A CLASS OF NONLINEAR SECOND-ORDER THREE-POINTS BOUNDARY VALUE PROBLEMS

In this paper, we establish two existence theorems of twin positive solutions for a class of nonlinear second-order three-point boundary value problems, and concentrate on the case when nonlinear term does not satisfy usual conditions.

POSITIVE SOLUTIONS OF SINGULAR SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM

In this paper, we obtain the existence of positive solutions for singular second-order Neumann boundary value problem by using the fixed point indices, the result generalizes some present results.

Positive Solutions for Nonlinear Second-Order Boundary Value Problem of Delay Differential Equation

In this paper, we study the nonlinear second-order boundary value problem of delay differential equation.. Without the assumption of the nonnegativity of f, we still obtain the existence of the positive solution.

The Technique of the Immersed Boundary Method: Application to Solving Shape Optimization Problem

We present a numerical method based on genetic algorithm combined with a fictitious domain method for a shape optimization problem governed by an elliptic equation with Dirichlet boundary condition. The technique of the immersed boundary method is incorporated into the framework of the fictitious domain method for solving the state equations. Contrary to the conventional methods, our method does not make use of the finite element discretization with obstacle fitted meshes. It conduces to overcoming difficulties arising from re-meshing operations in the optimization process. The method can lead to a reduction in computational effort and is easily programmable. It is applied to a shape reconstruction problem in the airfoil design. Numerical experiments demonstrate the efficiency of the proposed approach.

Existence of Positive Solutions of Generalized Sturm-Liouville Boundary Value Problems for a Singular Differential Equation

By employing the fixed point theorem of cone expansion and compression of norm type, we investigate the existence of positive solutions of generalized Sturm-Liouville boundary value problems for a nonlinear singular differential equation with a parameter. Some sufficient conditions for the existence of positive solutions are established. In the last section, an example is presented to illustrate the applications of our main results.

球内Dirichlet问题解及其应用

本文基于球内调和函数的 Ｄｉｒｉｃｈｌｅｔ 问题的球谐解式，推导了球内调和空间的 Ｐｏｉｓｓｏｎ 积分。将其应用于航空重力测量数据的向下延拓时，积分边界面是空中球面，边界值是空中重力异常或纯重力异常，推求地面重力异常可直接积分计算，而勿需像球外 Ｐｏｉｓｓｏｎ 积分那样迭代求解积分方程。

2n阶椭圆型复方程的Dirichlet边值问题

本文先使用解的先验估计和 Leray-Schauder 定理讨论了2u 阶非线性椭圆型复方程在单位圆上Dirichlet 边值问题的可解性.其次,使用积分方程的 Fredholm 定理讨论2u 阶线性椭圆型复方程上述边位问题的可解性.最后,我们还简略地讨论了两个未知实函敬的2n 阶线性与非线性椭圆型方程组的相应边值问题,在处理以上各边值问题时,都利用.关于方程 U_(?)=F(z)的 Dirichlet 边值问题解的积分表示式.

方程△u+g(|X|)f(u)=0的环上Dirichlet边值问题的正对径解的存在性

研究了二阶椭圆方程△ｕ＋ｇ（｜Ｘ＋）ｆ（ｕ）＝０在环域上关于Ｄｉｒｉｃｈｌｅｔ边界条件的正对径解的存在性．文中不要求ｌｉｍｆ（ｌ）／ｌ、ｌｉｍｆ（ｌ）／ｌ存在．文的工作推广了文［７］、９］中的结论．

半平面中的Dirichlet边值逆问题

给出半平面中解析函数的一类Dirichlet边值逆问题的数学提法.依据半平面中解析函数的D irichlet边值问题和广义D irichlet边值问题,讨论了此边值逆问题的可解性.利用半平面中解析函数D irichlet边值问题的Schwarz公式,给出了该边值逆问题的可解条件和解的表示式.

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。

C^n空间中的正则向量函数的Dirichlet边值问题

本文讨论了Ｃｎ空间中有界区域Ｄ上的２ｎ维正则向量函数（满足方程ＬＦ＝０，Ｌ＝∑ｎｋ＝１｜′×…×｜′×０／ｚｋ／ｚｋ０×｜×…×｜）的Ｄｉｒｉｃｈｌｅｔ边值问题，获得了边界值为Ｃ１类的２ｎ维复值向量函数的Ｄｉｒｉｃｈｌｅｔ边值问题的可解条件，同时还获得了Ｄ上的ｎ元解析函数的Ｄｉｒｉｃｈｌｅｔ问题的可解条件，并将以上结果应用到Ｃｎ空间中的超球与多圆柱区域上。