SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

AN EXISTENCE THEOREM OF POSITIVE SOLUTIONS FOR ELASTIC BEAM EQUATION WITH BOTH FIXED END-POINTS

By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.

New Results on Generalized c-Distance Without Continuity in Cone b-Metric Spaces over Banach Algebras

In this work,some new fixed point results for generalized Lipschitz mappings on generalized c-distance in cone b-metric spaces over Banach algebras are obtained,not acquiring the condition that the underlying cone should be normal or the mappings should be continuous.Furthermore,the existence and the uniqueness of the fixed point are proven for such mappings.These results greatly improve and generalize several well-known comparable results in the literature.Moreover,some examples and an application are given to support our new results.

POSITIVE SOLUTIONS TO AN m-POINT BOUNDARY VALUE PROBLEM

The existence of positive solutions for second order m-point boundary value problemx″-q(t)f(x,x′)x′=0, x(0)= m i=2 b ix(ξ i),x′(1)=αx′(0)are investigated,where ξ i,b i and α are constants satisfying 0=ξ 1<ξ 2<...<ξ m-1 <ξ m=1,b i≥0 for i=2,...,m with β∶= m i=2 b i∈[0,1), and α>1. Our approach is based on the fixed point theorem in cones.

Existence of Positive Solutions for Higher-Order Four-Point Boundary Value Problems with a p-Laplacian Operator

A class of higher-order four-point boundary value problems with a p-Laplacian operator is studied. By use of a fixed point theorem in cones, sufficient conditions for the existence of positive solutions for the boundary value problems are obtained.

Positive solutions to (n-1,1) m-point boundary value problems with dependence on the first order derivative

Using the extension of Krasnoselskii＇s fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green＇s function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.

EXISTENCE THEOREMS OF SOLUTIONS FOR NONLINEAR IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES

In this paper,the Monch fixed point theorem and an impulsive integral inequality is used to prove some existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces that improve and extend the previous results.

一类完全非线性四阶微分方程正周期解的存在性

讨论一类完全非线性四阶微分方程u^((4))(t)+a(t)u(t)=f(t,u(t),u′(t),u″(t),u″′(t))正周期解的存在性,其中,a(t)∈C([0,ω],(0,+∞)),f∈C([0,ω]×[0,+∞)×R^(3),[0,+∞)).在允许非线性项满足超线性增长不等式条件的情况下,利用Green函数和锥上的不动点理论,获得上述四阶微分方程正周期解的存在性结果,并通过例子验证了主要结果的有效性.

Positive Solutions of Four-order Dierence Equations with Two Point Boundary Value Problems

In this paper,by using the Krasnoselskii xed point theorem,we prove the existence one or multiple of positive solutions of fourth-ordernonlinear dierence equations with two point boundary value problem.

带有p-Laplacian算子的分数阶积分-微分方程边值问题正解的存在性

研究了带有p-Laplacian算子以及变Riemann-Liouville分数阶积分的分数阶积分-微分方程的边值问题,利用锥上的不动点定理,得到了该边值问题正解的存在性结果.

一类非线性四阶离散边值问题正解的存在性

在f满足超线性或次线性的条件下,通过运用锥上的不动点定理讨论非线性四阶离散边值问题正解的存在性,建立相应线性问题的格林函数并获得其性质.

带p-Laplace算子的离散混合边值问题负凸解的存在性

运用锥上的不动点定理讨论带p-Laplace算子的离散混合边值问题△[φ_(p)(△u(t-1))]=f(t,-u(t)),t∈[2,T-1]_(Z),△u(1)=0,u(T)=0负凸解的存在性,其中φ_(p)(s)=|s|^(p-2)s,p>1,f:[2,T-1]_(Z)×[0,+∞)→[0,+∞)连续.

一类k-Hessian系统三个径向解的存在性

在非线性项满足相应的条件时,运用Leggett-Williams不动点定理获得了带有权函数的k-Hessian系统三个径向解的存在性,并通过两个例子验证了所获结果的有效性.该结果是在非线性项去掉单调性的增长性条件下获得,在一定程度上推广了相关文献的结果.

一类非线性二阶半正周期问题正解的存在性

本文研究了非线性二阶半正周期问题{-u″(t)+a(t)u(t)=λg(t)(f(u)+ω(t))t∈(0,1)u(0)=u(1)u'(0)=u'(1)正解的存在性,其中λ为正参数,a:[0,1]→[0,∞),g:[0,1]→[0,∞)均为连续函数,ω是[0,1]上的连续函数且|ω(t)|≤k,f:[0,∞)→[0,∞)为连续函数且满足f0=limf(u)u→0 u=0,f∞=limf(u)u→∞u=∞.运用锥上不动点定理证明了:存在常数λ*>0,使得对于λ∈(0,λ*),该问题至少有一个正解.

变系数三阶周期边值问题的正解(英文)

研究了变系数非线性三阶周期边值问题的正解.非线性项可以关于空间变元奇异.利用适当的变换此问题被转换为一个Hammerstein积分方程,利用锥上的Guo-Krasno-selski不动点定理获得了1～2个正解的存在性.

EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.

MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE

In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SUPERLINEAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE

In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

Three positive doubly periodic solutions of a nonlinear telegraph system

This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system.