非共振奇异超线性边值问题正解存在的充分必要条件

本文研究非共振奇异超线性边值问题正解的存在性,利用锥上的不动点定理给出了非共振奇异超线性边值问题有C1[0,1]正解存在的充分必要条件.     

MULTIPLE POSITIVE SOLUTIONS TO FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS

In this paper,using the Krasnaselskii's fixed point theory in cones and localization method,under more general conditions,the existence of n positive solutions to a class of fourth-order singular boundary value problems is considered.     

POSITIVE SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEM OF SECOND ORDER

Some results of existence of positive solutions for singular boundary value problems{-u"(t)=p(t)f(u(t)), t∈(0,1), u(0)=u(1)=0are given, where the function p(t) may be singular at t = 0, 1.     

EXISTENCE OF POSITIVE SOLUTION TO SUPERLINEAR SEMIPOSITONE SINGULAR m-POINT BOUNDARY VALUE PROBLEMS

Sufficient conditions for the existence of positive solution to superlinear semi-positone singular m-point boundary value problem are given by cone expansion and compression theorem in norm type.     

半正泛函微分方程边值问题的正解

本文证明了一个关于一类含参数半正奇异泛函微分边值问题正解的存在性结果。推广了已有的某些结果。作为应用,讨论了一个含参数多项式型泛函微分方程正解的存在性问题。     

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.     

高阶微分方程边值问题的多个正解存在性

本文利用五个泛函的不动点定理,研究一类2n阶微分方程边值问题的多个单调正 解的存在性.     

POSITIVE SOLUTIONS TO SINGULAR SECOND ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH SIGN-CHANGING NONLINEARITIES

This paper deals with the existence of positive solutions to the singular secondorder periodic boundary value problem. We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.     

TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: -u′′(t) = λf(t, u(t)) for all t ∈ (0, 1) subjecting to u(0) = 0 and αu(η) = u(1), where η∈ (0, 1), α∈ [0, 1), and λ is a positive parameter. The nonlinear term f(t, u) is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ* ∈ (0, +∞], such that the above problem has at least two positive solutions for any λ∈ (0, λ*) under certain conditions on the nonlinear term f.     

具有变号非线性项的二阶三点边值问题的两个正解

本文首先证明双锥上的一个不动点定理，并通过该定理研究一类具有变号非线性项的二阶三点边值问题两个正解的存在性．同时，该三点边值问题相关的Green函数也被给出．     

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。     

Banach 空间中奇异积分-微分方程边值问题多解的存在性

通过建立一个特殊的锥,运用锥拉伸与锥压缩不动点定理,获得了Banach空间中一类非线性混合型奇异积分-微分方程边值问题多解的存在性．     

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     

Sturm-Liouville方程奇异边值问题的正解

本文利用不动点指数理论,讨论Sturm-Liouville方程(p(t)u'(t))'+g(t)F(t,u)=0 奇异边值问题的正解的存在性.     

MULTIPLE POSITIVE SOLUTIONS TO SOME SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEMS

Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these problems are also given.     

二阶奇异边值问题两个非负解的存在性

利用拓扑度理论,给出了边值问题ｕ″（ｔ）＋λａ（ｔ）ｆ（ｕ（ｔ））＝０,０〈ｔ〈１,ａｕ（０）－βｕ’（０）＝０,γｕ（１）＋δｕ’（１）＝０两个非负解的存在性结果,这里允许ａ在ｔ＝０和ｔ＝１处有奇性。     

POSITIVE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND ORDER DIFFERENTIAL SYSTEMS

In this paper, by utilizing a fixed point theorem on cone in Banach space, the author disscusses the periodic boundary value problem of second order differential systems. Some results on the existence of positive solutions are derived.     

EXISTENCE THEOREM ABOUT MULTIPLE POSITIVE SOLUTIONS TO p-LAPLACIAN BOUNDARY VALUE PROBLEM

In this paper,we apply a fixed point theorem to verify the existence of multiple positive solutions to a p-Laplacian boundary value problem.Sufficient conditions are established which guarantee the existence of multiple positive solutions to the problem.     

POSITIVE SOLUTIONS OF NONLINEAR FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS

By constructing a special cone and using the fixed point theorem of cone expansion and compression,this paper investigates fourth-order singular boun- dary value problems with sublinear effect and presents some necessary and sufficient conditions for existence of C~2 or C~3 positive solutions.Further,some examples are given concerning the applications of our main results.     

MULTIPLE POSITIVE SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN

This paper is concerned with the existence of positive solutions to singular boundary value problems of functional differential equations with p-Laplacian. Under the suitable conditions,the existence of three positive solutions is esta- blished by using an abstract fixed point theorem.