Compression-expansion fixed point theorem in two norms and applications

In this paper we present a two-norms version of Krasnoselskii's fixed point theorem in cones. The abstract result is then applied to prove the existence of positive Lp solutions of Hammerstein integral equations with better integrability properties on the kernels.     

Existence of multiple symmetric positive solutions of higher order Lidstone problems

This paper gives the sufficient conditions of the existence of at least three symmetric positive solutions for one type of higher order autonomous Lidstone problem by applying the five functionals fixed point theorem. The analogous result for higher order nonautonomous singular Lidstone problem is also proved here.     

Schaefer type theorem and periodic solutions of evolution equations

Two fixed point theorems for the sum of contractive and compact operators are obtained in this paper, which generalize and improve the corresponding results in [H. Schaefer, Über die methode der a priori-Schranken, Math. Ann. 129 (1955) 415-416; T.A. Burton, Integral equations, implicit functions and fixed points, Proc. Amer. Math. Soc. 124 (1996) 2383-2390; V.I. Istrǎtescu, Fixed Point Theory, an Introduction, Reidel, Dordrecht, 1981; T.A. Burton, K. Colleen, A fixed point theorem of Krasnoselskii-Schaefer type, Math. Nachr. 189 (1998) 23-31; D.R. Smart, Fixed Point Theorems, Cambridge Univ. Press, Cambridge, 1980]. As the applications for the results, we obtain the existence of periodic solutions for some evolution equations with delay, which extend the corresponding results in [T.A. Burton, B. Zhang, Periodic solutions of abstract differential equations with infinite delay, J. Differential Equations 90 (1991) 357-396].     

双锥不动点定理及其在非线性边值问题中的应用

本文研究了具可变号非线性项的非线性边值问题的正解存在性,推广了 Krasnoselskii 不动点定理,得到了新的锥上不动点定理,并应用这些定理给出这类边值问题正解的存在性．     

Existence of a fixed point for a semicontinuous operator and its application

We employ a partial order method and cone theory to prove an existence theorem for a fixed point for a semicontinuous operator; also the decreasing and increasing semicontinuous operators are studied.     

关于正映射锥上不动点指标的一个猜想

本文在一些附加条件下证明了Dancer E.N.提出的一个关于正映射锥上不 动点指标计算的猜想,并举例说明其应用.     

Eigenvalue problem for p-Laplacian three-point boundary value problems on time scales

Let T be a time scale such that 0,T∈T, β,γ?0 and 0<η<ρ(T). We consider the following p-Laplacian three-point boundary problem on time scales

     

二阶非线性常微分方程积分边值条件四点边值问题正解

本文证明二阶非线性常微分方程积分边值条件四点边值问题正解的存在性。     

A NOVEL FIXED POINT THEOREM AND ITS APPLICATIONS

In this article, a novel fixed point theorem in C[0,1] space is established by using the properties of fixed point index. This theorem is then applied to prove the existence of positive solutions for three-point boundary value problems and generalizes some previous results.     

Positive solutions of fourth-order boundary value problems with two parameters

In this paper the existence results of positive solutions are obtained for fourth-order boundary value problem

u(4)+βu″−αu=f(t,u),0<t<1,u(0)=u(1)=u″(0)=u″(1)=0,     

非局部边值条件下一类四阶问题的正解

本文研究一类非局部边值条件下非线性项含有二阶导数的四阶问题.利用一个特殊锥上的不动点指数理论,在非线性项满足关联谱半径的一些不等式条件时,获得该问题正解存在的结果.给出了具有变号系数多点形式和变号核积分形式的混合边值条件下的两个例子来说明理论结果的应用.     

非线性二阶常微分方程的正周期解

讨论一类非线性二阶常微分方程的周期解问题 ,利用Banach空间锥上的不动点定理得到了正周期解的存在性和多重性结果 ,大大改进了文献 [1 ]的结果     

A compression type mountain pass theorem in conical shells

In this paper we present a compression type version of the mountain pass lemma in a conical shell with respect to two norms. An application to second-order ordinary differential equations is included.     

A generalization of the Leggett-Williams fixed point theorem and its application

A generalization of the Leggett-Williams fixed point theorem is established. As an application, the existence of multiple nondecreasing positive solutions for a class of third-order m-point boundary value problems is obtained.     

Ekeland变分原理的推广及Caristi不动点定理在半度量空间的推广形式

本证明了半度量空间中的Ekeland变分原理及Caristic不动点定理．进而证明了半度量空间中的压缩映像原理。     

Fixed point theorems and convergence theorems for some generalized nonexpansive mappings

We introduce some condition on mappings. The condition is weaker than nonexpansiveness and stronger than quasinonexpansiveness. We present fixed point theorems and convergence theorems for mappings satisfying the condition.     

POSITIVE PERIODIC SOLUTIONS OF FIRST AND SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u"(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u"(f)=f(t,u(t)) (t∈R), where f: R×R~ →Ris a continuous function which is ω-periodic in t. The discussion is based on the fixedpoint index theory in cones.     

Positive solutions for nonlinear three-point boundary value problems on time scales

Let T be a time scale such that 0,T∈T. Consider the following three-point boundary value problem on time scales:

     

Fixed point theory for generalized contractions in cone metric spaces

In this paper, we prove some fixed point theorems for generalized contractions in cone metric spaces. Our theorems extend some results of Suzuki (2008) [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc Amer Math Soc 136(5) (2008), 1861-1869] and Kikkawa and Suzuki (2008) [M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal 69(9) (2008), 2942-2949].