非线性多孔介质流动模型问题的分歧

本文讨论一类多孔介质流动模型非线性边值问题．对这类问题以及广泛的一类算子方程，我们得到了渐近歧点的存在性     

具有奇性的一类边值问题的正解

讨论一类奇异二阶微分方程的边值问题，给出了正解存在和不存在的准则。     

一类高阶方程正解的存在唯一性

讨论了一类2n阶方程的边值问题,得到了该问题存在唯一正解的充分条件.     

一类边值问题正解的确切个数

利用打靶法给出了一类边值问题x″(t)=λxα(t),t∈(0,1),x(0)=x(1)=0正解的确切个数,得到了(i)当λ<0,α>-1且α≠1时,该边值问题只有唯一的正解;(ii)当λ<0且α<-1时,该边值问题没有正解等结论.     

一类两点边值问题正解的个数

讨论边值问题（（一v＇（r））~n）＇=λ（v~α＋v~β）,v＇（0）=v（1）=0,其中λ〉0是正参数.对（n-α）（n-β）〉0的情形得出了正解的存在唯一性.对0〈α〈n〈β的情形得到,存在λ~＊〉0,使得当0〈λ〈λ~＊时,此边值问题恰好存在两个正解;当λ=λ~＊时,此边值问题存在唯一一个正解;当λ〉λ~＊时,此边值问题不存在正解.     

一类四阶奇异边值问题的正解

本文讨论了如下四阶奇异边值问题正解的存在性(?)其中p可能在t=0,1都有奇点.     

一类Dirichlet边值问题的正解存在性

本文对Ｄｉｒｉｃｈｌｅｔ边值问题ｙ″－ｆ（ｔ，ｙ）＝０，ｙ（０）＝ｃ＞０，ｙ（１）＝ ０，给出正解的存在性结论，其中函数ｆ（ｔ，ｙ）可以是变号函数，并且可能在ｙ＝０处具有奇异性．     

一类两点边值问题的正解个数

本文讨论边值问题y"+λ(yp+μy+yq)=0,y(-1)=y(1)=0,其中λ＞0是正参数,μ≥0.对(1-p)(1-q)＞0的情形得出了正解的存在唯一性.对(1-p)(1-q)＜0的情形,其主要结论是若p＞1＞q＞-(25+23p)/(23+25p),μ≥0,则存在λ*＞0,使得当0＜λ＜λ*时,此边值问题恰好存在两个正解,当λ=λ*时,存在唯一正解,当λ＞λ*时,不存在正解.     

一类高阶奇异边值问题的正解

本文利用上下解方法给出一类高阶微分方程的奇异边值问题正解的充分条件，改进并推广了韦忠礼在文献［１］中的结果，并指出其证明的漏洞．     

POSITIVE SOLUTIONS OF m-POINT BOUNDARY-VALUE PROBLEMS

The paper is concerned with the existence and multiplicity of positive solutions for a nonlinear m-point boundary value problem. The proofs are based on a fixed-point theorem and a fixed-point index theorem in cones.     

EXISTENCE OF POSITIVE RADIAL SOLUTIONS AND ENTIRE SOLUTIONS FOR QUASILINEAR SINGULAR BOUNDARY VALUE PROBLEMS

ＥＸＩＳＴＥＮＣＥＯＦＰＯＳＩＴＩＶＥＲＡＤＩＡＬＳＯＬＵＴＩＯＮＳＡＮＤＥＮＴＩＲＥＳＯＬＵＴＩＯＮＳＦＯＲＱＵＡＳＩＬＩＮＥＡＲＳＩＮＧＵＬＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＹａｎｇＺｕｏｄｏｎｇ（杨作东）＆ＧｕｏＺｏｎｇｍｉｎｇ（郭...     

MULTIPLE POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF DELAY DIFFERENTIAL EQUATIONS WITH DENUMBERABLE SINGULARITIES ON INFINITE INTERVAL

This paper deals with the existence of denumberable positive solutions to boundary value problems of delay differential equations with denumberable singularities on infinite intervals. By the fixed-point index theory and a new fixed-point theorem in cones, the existence of denumberable positive solutions is obtained under some suitable growth conditions imposed on the nonlinear term.     

TWO POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR BOUNDARY VALUE PROBLEMS

An existence theorem of two positive solutions of the singular BVP1/(p(t))(p(t)y′(t))′+λα(t)f(y(t))=0,t∈(0,1),αy(0)-βp(t)y′(t)=0=γy(1)+δp(t)y′(t)was established by using topological degree theory.     

EXISTENCE OF TRIPLE POSITIVE SOLUTIONS TO A MULTI-POINT BOUNDARY VALUE PROBLEM

We apply a fixed point theorem to verify the existence of at least three positive solutions to a multi-point boundary value problem with p-Laplacian. Existence criteria which ensure the existence of triple positive solutions are established.     

奇异高阶积分边值问题正解的全局结构

本文研究了带Riemann-Stieltjes积分边值条件的奇异高阶积分边值问题正解的全局分歧结构.利用相关文献,获得了此类问题的格林函数并推证其满足的性质,同时可获得此类问题等价于一个全连续算子方程;其次,在满足所给的条件时,利用Krein-Rutmann定理建立了此类问题对应的线性问题存在简单的主特征值;最后,当非线性项在零和无穷远处满足非渐进线性增长条件、参数满足不同范围的值时,利用Dancer全局分歧定理、Zeidler全局分歧定理和序列集取极限的方法,建立了此类问题正解的全局结构,进而获得了正解的存在性,推广了文献[8]中的主要结果.     

EXISTENCE OF POSITIVE SOLUTIONS TO A SINGULAR THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, we study a singular third-order three-point boundary value problem. By using a fixed-point theorem of cone expansion-compression type, we establish results on the existence of at least one, at least two, and $n$ positive solutions to the boundary value problem. Finally we give an example.     

MULTIPLE POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

This paper is concerned with the boundary value problem for a system of nonlinear third order differential equations. Under some suitable conditions, the existence and multiplicity of the positive solutions are established by using abstract fixed-point theorems.     

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO NONLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM

In this paper, we study a nonlinear semipositone Neumann boundary value problem. Under some suitable conditions, we prove the existence and multiplicity of positive solutions to the problem, based on Krasnosel’skii’s fixed point theorem in cones.     

具p-Laplacian算子型奇异边值问题多重正解

本文讨论了一类具ｐ－Ｌａｐｌａｃｉａｎ算子型奇异边值问题（φｐ（ｘ＇））＇＋ａ（ｔ）ｆ（ｘ（ｔ））＝０,ｘ（０）－βｘ（０′）＝ ０,ｘ（１）＋ δｘ′（１）＝０多重正解的存在性,其中φｐ（ｘ）＝｜ｘ｜ｐ－２ｘ,ｐ＞１ 通过使用不动点指数定理, 在适当的条件下,建立了这类边值问题存在多重正解的充分条件．这些结果能被用来研究椭圆边值问 题多重径向对称解的存在性．