一类四阶奇异边值问题对称正解的最优存在性

本文研究了一类四阶奇异边值问题.通过建立一个特定的锥,利用Leggett-Williams不动点定理,从而在一定的条件下得到一类四阶奇异边值问题对称正解的最优存在性,推广了奇异边值问题对称正解的最优存在性的结果.     

一类二阶m点边值问题的正解

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.     

MULTIPLE POSITIVE SOLUTIONS OF NONRESONANT SINGULAR BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

This paper studies the existence of multiple positive solutions of nonresonant singular boundary value problem of second order ordinary differential equations. A sufficient condition for the existence of C[0,1] multiple positive solutions as well as C1[0, 1] multiple positive solutions is given by means of the fixed point theorems on cones.     

时间标度上的动态方程周期边值问题的正解

讨论了时间标度上一类二阶非线性动态方程的周期边值问题正解以及多解的存在性,利用锥上的不动点理论给出了简捷的判别方法并举例。     

Existence of positive solutions to a boundary value problem for a delayed singular high order fractional differential equation with sign-changing nonlinearity

In this paper, we discuss the existence of positive solutions to the boundary value problem for a high order fractional differential equation with delay and singularities including changing sign nonlinearity. By using the properties of the Green function, Guo-krasnosel"skii fixed point theorem, Leray-Schauder"s nonlinear alternative theorem, some existence results of positive solutions are obtained, respectively.     

四阶边值问题正解的存在性与多解性

本文讨论了非线性四阶边值问题u^(4)(t)=φ（t）f(u(t),u“(t),t∈(0,1),u(0)=u(1)=u“(0) =u“(1)=0正确的存在性，其中φ（t)∈C([0,1],[0,∞)),f(u,v)∈C（[0,∞],[0,∞))。利用锥压缩与锥拉伸不动点定理，给出了该问题正解存在与多个正解存在的充分条件。     

非线性边值问题正解存在性的特征值判据

讨论了二阶常微分方程边值问题{-u~n(t)=f(t,u(t)),t∈[0,1],u(0)=u(1)=0正解的存在性,其中f:[0,1]×R~+→R~+连续.给出了该问题存在正解的新特征值判据,该判据改进了以前文献中的相关结果.我们的论证基于锥上的不动点指数理论.     

POSITIVE SOLUTION TO THREE-ORDER BOUNDARY VALUE PROBLEM WITH DEPENDENCE ON THE FIRST ORDER DERIVATIVE

By cone theory and the fixed point index,we study the existence of positive solutions to a three-order boundary value problem with dependence on the first order derivative.     

带$p$-Laplacian的四阶四点奇异边值问题的正解

In this paper, we consider the existence of positive solutions for the singular fourthorder four point boundary value problem with p-Laplacian operator. By using the fixed point theorem of cone expansion and compression, the existence of multiple positive solutions is obtained.     

半直线上耦合系统边值问题三个正解的存在性

讨论了半直线上非线性耦合系统边值问题,应用Leggett-Williams不动点定理,得到了三个正解的存在性结果,推广并改进了现有结果.     

四阶奇异边值问题两个正解的存在性

本文利用锥压缩和锥拉伸不动点定理,给出了四阶微分方程奇异边值问题两 个C2[0,1]和C3[0,1]正解的存在性.     

时间尺度上二阶动力方程三点边值问题解的存在性

运用锥中twin不动点定理,讨论了时间尺度上二阶动力方程三点边值问题至少有两个正解存在的条件．     

Existence of Positive Solutions for Second-Order m-Point Boundary Value Problems on Time Scales

This paper investigates thc existence of positive solutions of the m-point boundary value problem for second-order dynamic equations on time scales, and obtain the result that the problem has at least one positive solution by using functional-type cone expansion-compression fixed point theorem.     

半正定差分方程正解的存在性

利用锥压缩与锥拉伸不动点定理,在非线性项具有负下界和非减性条件下,讨论了一类二阶半正定非线性差分方程正解的存在性,改进和推广了现有差分方程的一些结果,并将所获得的结果应用于一个具体的二阶半正定非线性差分方程中.     

On the semilinear reaction diffusion system arising from nuclear reactors

In this work, the initial-boundary value problem for a class of semilinear reaction-diffusion systems is considered. By an abstract fixed point theorem on positive cone together with an accurate a priori estimate, we establish the coexistence of the positive stationary solutions and the uniqueness of ordered positive stationary solutions. Next, we study the global existence and blowup of positive solutions and obtain a threshold result. Finally, we give the blowup rate estimate of positive blowup solutions.     

抽象空间中一类带奇异性的混合型积分-微分方程边值问题的正解

利用不动点指数理论,研究了Banach空间中一类带奇性的混合型积分——微分方程边值问题正解的存在性,得到了多个正解存在的充分条件,并给出了相应的例子以说明所得结果的合理性和应用性.     

A THEOREM OF TRIPLE POSITIVE SOLUTIONS FOR MULTI-POINT BOUNDARY VALUE PROBLEMS

In this paper we prove a new fixed point theorem in cones and then obtainthe existence of triple positive solutions for a class of multi-point boundaryvalue problem.     

POSITIVE SOLUTIONS OF SINGULAR SUPERLINEAR SECOND ORDER BOUNDARY VALUE PROBLEMS

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非局部 Sturm-Liouville 型边值条件下四阶方程的正解

在本文中我们研究带Stieltjes积分的非局部Sturm-Liouville型边值条件下四阶问题, 其非线性项含有一阶和二阶导数. 利用在一个特殊锥上的不动点指数方法, 对于非线性项提出了一些不等式条件, 它们保证了该问题正解的存在性.给出了在具有变号系数多点和变号核积分的混合边值条件下几个例子来支持主要结论.     

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.