POSITIVE SOLUTIONS TO A NONHOMO- GENEOUS NONAUTONOMOUS SECOND- ORDER BOUNDARY VALUE PROBLEM

The existence of multiple positive solutions is studied for a nonlinear nonauto- nomous second-order boundary value problem with nonhomogeneous boundary con- ditions. In order to describe the growth behaviors of nonlinearity on some bounded sets, two height functions are introduced. By considering the integrals of the height functions and applying the Krasnosel＇skii fixed point theorems on a cone, several new results are proved.     

Positive Solutions of Nonlinear Elliptic Equations in Unbounded Domains in R 2

We study the existence of positive solutions of the nonlinear equation u+f(,u)=0, in D with u=0 on D, where D is an unbounded domain in R ² with a compact nonempty boundary D consisting of finitely many Jordan curves. The aim is to prove an existence result for the above equation in a general setting by using potential theory.     

CLASSIFICATION AND EXISTENCE OF POSITIVE SOLUTIONS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAY DEPENDING ON THE UNKNOWN FUNCTION

A class of second order nonlinear differential equations with delay depengingon the unknown function of the from(r(t)ψ(x(t))x' (t))' f (t, x(t), x (△ (t, x(t)))) = 0in the case where ∫∞0 ds/r(s) ＜∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also obtained.     

关于非线性特征值问题的一个正解存在定理

本文利用锥上的Krasnosel‘ skii不动点定理考察了一类非线性特征值问题，获得了这个问题的一个正解存在定理。     

奇异非线性二阶诺伊曼边值问题正解个数的研究

本文主要研究奇异非线性二阶诺伊曼边值正解的个数问题.利用比较定理,最大值原理和上界方法,得出了在一定条件下,该问题恰好有奇数个正解的结果.     

半线性奇摄动椭圆型方程边值问题的渐近解

本文运用了边界层函数构造了一类半线性奇摄动椭圆型方程边值问题解的渐近展开式，并证明了该展开式达到任一精度的一致有效性．     

一类多重调和方程的正整解的存在性及其性质

该文以Schauder-Tychonoff不动点定理为工具,建立了一类R^n上带奇异性的非线性多重调和方程正整解的存在性定理,并给出了解的有关性质,所得的结果丰富和发展了已有的理论和应用。     

一类R^2上奇异非线性多重调和方程的正整解

以Ｓｃｈａｕｄｅｒ－Ｔｙｃｈｏｎｏｆｆ不动点定理为工具,建立了一类平面上奇异非线性多重调和方程正的径向对称整体解的存在性定理,并给出了解的有关性质。     

EXISTENCE AND NONEXISTENCE OF POSITIVE SOLUTIONS TO A THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, we are concerned with the existence and nonexistence of positive solutions to a three-point boundary value problems. By Krasnoselskii’s fixed point theorem in Banach space, we obtain sufficient conditions for the existence and non-existence of positive solutions to the above three-point boundary value problems.     

关于R^2上的半线性双调和方程的正的整体解

本文研究一类平面上半线性双调和方程的正经向对称的整体解的存在性及解的性质，拓广了文〔１〕、〔２〕的结果。     

具状态时滞的高阶非线性微分方程正解正在性及分类

本文研究一类形如(r(t)x(n-1)(t))′+f(t,x(t), x(Φ(t,x(t)))=0的具状态时滞的高阶非线性微分方程. 按照最终正解的量级给出了它们的分类及存在的充分条件.     

NONEXISTENCE OF POSITIVE SOLUTIONS FOR A FOUR-POINT BOUNDARY VALUE PROBLEM FOR FRACTIONAL DIFFERENTIAL EQUATION

In this paper, we investigate the nonexistence of positive solutions for a class of four-point boundary value problem of nonlinear differential equation with fractional order derivative. We give sufficient conditions on nonlinear term and the parameter such that the boundary value problem has no positive solutions. Some examples are presented to illustrate the main results.     

TWO POSITIVE PERIODIC SOLUTIONS OF NONLINEAR INTEGRAL EQUATION ON THE INFINITE INTERVAL MODELLING INFECTIOUS DISEASE

In this paper, by applying Avery-Henderson fixed point theorem in a cone, we establish some new existence results of two positive periodic solutions for a type of nonlinear integral equations with variant delay.     

On a semilinear parabolic equation

We introduce a general class of potentials so that the semilinear parabolic equation in , , has global positive continuous solutions. These results extend the recent ones proved by Zhang to a more general class of potentials.

     

POSITIVE SOLUTION FOR NONLINEAR SINGULAR BOUNDARY VALUE PROBLEMS

Under suitable conditions on f(·,u), it is shown that the two-point boundaryvalue problem((u'))' + λq(t)f(u) = 0in (0, 1),u(0) = u(1) = 0,has two positive solution or at least one positive solution for λ in a compatibleinterval.     

半导体物理中的一个两点边值问题

本文研究了在半导体流的区域提纯过程中提出的两点边值问题解的存在性，我们用上、下解方法和Ｓｓｈａｕｄｅｒ不动点定理证明了如果Ｑ＝２Ａ３Ｒｅ，其中Ａ是表面速率，Ｒｅ是Ｒｅｙｎｏｌｄｓ数，则当０ Ｑ １２．６８时，该问题有解． 对［１］的结果（０ Ｑ＜８．５１时，此问题的解存在）进行了重要的改进．     

EXISTENCE OF AT LEAST THREE POSITIVE SOLUTIONS TO MULTI-POINT BOUNDARY VALUE PROBLEM WITH p-LAPLACIAN OPERATOR

In this paper,we consider a multi-point boundary value problem. We obtain suffcient conditions ensuring the existence of at least three positive solutions to the boundary value problem.     

一类具变号非线性项二阶m点边值问题的正解

利用一个新的不动点定理,研究一类具有变号且依赖一阶导数非线性项二阶m点边值问题正解的存在性,得到了正解存在的充分条件.     

二阶奇异初值问题正解

应用不动点定理和逼近方法,研究了二阶非线性奇异初值问题正解的存在性,获得了若干新结果。