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.     

一类非线性p-Laplace边值问题的正解

应用锥理论和不动点指数方法,在与相应齐次增算子的第一特征值相关的条件下,得到了下述非线性p-Laplace边值问题{(|u″|p-1u″)"=f(t,u),t∈(0,1),u(0)=u(1)=u″(0)=u″(1)=0的正解,改进了相关文献中的结论     

一类非负二次整数规划问题的分支定界缩减方法

针对一类非负整数二次规划问题,提出了一个新的分枝定界缩减方法.在这个方法里,使用了一个新的超矩形二分技术和一个新的线性规划松弛定下界技术,同时为了提高逼近程度和加快收敛速度,使用了超矩形缩减策略.数值结果表明所提出的算法是可行的和有效的.     

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

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

一类广义解析函数的Riemann边值逆问题

本文给出了一类有关广义解析函数Riemann边值逆问题的数学提法．在将此边值逆问题转化为边值问题的基础上，借助于广义解析函数边值问题的相关理论，分别获得了此边值逆问题在正则型和非正则型情况下的解．     

MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS

In this paper, we are concerned with the following problem:(-△)ku = λf(x)|u|q-2u + g(x)|u|k*-2u, x ∈Ω,u ∈ Hk0(Ω),where Ω is a bounded domain in RNwith N ≥ 2k + 1, 1 q 2, λ 0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k* =2N N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.     

一类椭圆方程很弱解关于区域的连续性

本文讨论了二阶椭圆型方程－Δｕ＝ｆ（ｘ,ｕ）,ｘ∈Ω的Ｄｉｒｉｃｈｌｅｔ问题ｕ｜Ω＝０的很弱解ｕ∈Ｗ０１,ｒ（Ω）（１＜ｒ＜２）关于区域Ω的连续性及很弱边值问题的很弱解的唯一性．     

SOME NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS FOR THIRD ORDER SINGULAR SUBLINEAR MULTI-POINT BOUNDARY VALUE PROBLEMS

We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x(3)(t) + f(t, x(t), x′(t)) = 0, 0 t 1,x(0)-m1∑i=1 αi x(ξi) = 0, x′(0)-m2∑i=1 βi x′(ηi) = 0, x′(1)=0,where 0 ≤ ai≤m1∑i=1 αi 1, i = 1, 2, ···, m1, 0 ξ1 ξ2 ··· ξm1 1, 0 ≤βj≤m2∑i=1βi1,J=1,2, ···, m2, 0 η1 η2 ··· ηm2 1. And we obtain some necessa βi =11, j = 1,ry and sufficient conditions for the existence of C1[0, 1] and C2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f(t, x, y)may be singular at x, y, t = 0 and/or t = 1.     

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.     

一类两点边值问题的正解个数

本文讨论边值问题y'+λ(yp+μp+yp)=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.     

MULTIPLE POSITIVE SOLUTIONS OF A CLASS OF THREE-POINT SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper, the existence theorem for three positive solutions is presented for the singular nonlinear boundary value problem by applying the extended Five Functionals fixed point theorem. singular nonlinear boundary value problem; positive solutions; cone; fixed point theorem     

SOLUTIONS FOR SUPERLINEAR(n-1,1)CONJUGATE BOUNDARY VALUE PROBLEMS

1 IntroductionIn this paPer) we are concerned with positive and nontrivial solutions for superlinear (n -1, 1) conjugate boundary value problem:where f: [0, 1] x R1 - R1 is continuous.In case n = 2, (1) describes various phenomena, such as nonlinear diffusion generated -by nonlinear $ourcesl thermal ignition of gases, and concentration in chendcal or biologicalproblems, see, for examPle [1-5]. Also, [6] used the second order case in modeling the one-dimensional Dirichlet problem;In case f(x,…     

NONTRIVIAL SOLUTIONS TO SINGULAR BOUNDARY VALUE PROBLEMS FOR FOURTH-ORDER DIFFERENTIAL EQUATIONS

The singular boundary value problems for fourth-order differential equations are considered under some conditions concerning the first eigenvalues of the relevant linear operators. Sufficient conditions which guarantee the existence of nontrivial solutions are obtained. We use the topological degree to prove our main results.     

半正脉冲微分边值问题的多重正解

本文证明了几个关于半正脉冲奇异微分边值问题多重正解的存在性结果.     

一类2n阶次线性奇异边值问题的正解

利用单调迭代方法给出了一类2n阶次线性奇异常微分方程正解的存在性,得到C~(2n-2)[0,1]和C~(2n-1)[0,1]正解存在的充分必要条件,也得到正解的唯一性.     

一类多参数Semipositone问题的多个正解

本文在一般有界区域上研究了一类多参数Semipositone问题.结合上下解方法与下降流不变集临界点理论,证明了此类问题有四个解,其中至少有两个是正的.     

POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER DELAY DIFFERENTIAL EQUATION

In this paper,we discuss the existence of positive solutions of the second- order delay boundary value problems.By applying the fixed-point theorem in a cone,we show the existence of at least one positive solution with singularity and the superlinear semipositone.As an application,we also give some examples to demonstrate our results.     

一类非线性波动方程的显式精确解

本文用直接方法和假设的一种结合求出了一类较广泛的非线性波动方程ｕｔｔ－ａ１ｕｘｘ＋ａ２ｕｔ＋ａ３ｕ＋ａ４ｕＳ＾２＋ａ５ｕ＾３＝０的一些显式精确行波解,贱个有重要的非线性数学物理方程,如φ＾４方程,Ｋｌｅｉｎ－Ｇｏｒｄｏｎ方程,Ｓｉｎｅ－Ｇｏｒｄｏｎ方程,及Ｓｉｎｈ－Ｇｏｒｄｏｎ方程的近似,Ｌａｎｄａｕ－Ｇｉｎｚｂｕｒｇ－Ｈｉｇｇｓ方程,Ｄｕｆｆｉｎｇ方程,非线性电报方程等都可作为该方程的特殊情形得     

PERIODIC SOLUTIONS FOR A CLASS OF DELAYED NONLINEAR DIFFERENCE EQUATIONS

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree,some sufficient conditions are established for the global existence of positive periodic solutions of a class of delayed nonlinear difference equations.     

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.