Global Generalizations of the Birkhoff-Kellogg Theorem on Set-Contraction Operators

The purpose of this paper is to give some global generalizations of the Birkhoff—Kellogg theorem on set-contraction operators.In this paper,we 8uppose that X is an infinite-dimensional Banach space and A:x→X is a κ-set-contraction operator,0≤κ< ∞.we shall denote by E the Banach space R~1×X with norm ‖(λ,χ)‖=(λ~2 ‖χ‖~2)~1/2.The c1losure of the set of nonZero solutions of the equation χ=λAχ will be denoted by L,i.e.,     

两点拉伸型不动点定理及其应用

在研究各种非线性方程解的存在性问题时,上下解方法是一个强有力的工具.设 E是 Banach 空间,P 是 E 中的锥,E 中的半序由 P 导出.设 A:E→E 是一个算子.如果x_0∈E 满足     

Caristi 不动点定理的推广及应用

本文推广了古典的Garisti不动点定理,作为应用,古典的Ekeland变分原理得到了推广,并且证明了推广的Garisti不动点定理和推广的Ekeland变分原理是等价的．     

非线性算子方程变号解的存在性及其应用

本文利用锥理论讨论了非线性算子方程变号解的存在性,并将抽象结果应用于Sturm-Liouville两点边值问题。所得结果无论在理论上还是在应用上都是新的.     

关于Hammerstein型非线性积分方程固有值的一点注记

Let Aφ(x)=∫_GK(x,y)f(y,φ(y))dy, where G is a bounded closed domain in Euclidean space, K(x,y) is continuous on G×G, f(x,u) is continuous on G×R, and f(x,0)≡0. Set G_x={x|x∈G,K(x,y)≠0},G_y={y|y∈G,K(x,y)≠0},G₁=G_x∩G_y≠φ.Let K₁(x,y) be the restriction of K(x,y) on G₁×G₁,f₁(x,u)be the restriction of f(x, u) on G₁× R, and A₁φ=∫_G1K₁(x,y)f₁(y,φ₁(y))dy, The main result of this paper is Theorem λ≠0 is an eigenvalue of A, if and only if λ is an eigenvalue of A₁.     

THE RELATION BETWEEN SIGN-CHANGING SOLUTION AND POSITIVE-NEGATIVE SOLUTIONS FOR NONLINEAR OPERATOR EQUATIONS AND ITS APPLICATIONS

By fixed point index theory and a result obtained by Amann, existence of the solution for a class of nonlinear operator equations x=Ax is discussed. Under suitable conditions, a couple of positive and negative solutions are obtained. Finally, the abstract result is applied to nonlinear Sturm-Liouville boundary value problem, and at least four distinct solutions are obtained.     

Banach空间中某些新的列紧性判别法及其应用

本文研究了半序Banach空间E的范数拓扑与弱拓扑的关系,给出了E的全序子集列紧性的若干判别定理,并讨论了在Pareto最优问题、不动点理论和计算数学上的应用。     

含不连续项的常微分积分方程的解

本文研究微分积分方程 u'=g(t,u)+integral from 0 to 1(k(t,s)f(s,u(s))ds),u(0)=x_0最小解、最大解的存在性.本文的特点是关于方程中函数g(t,x),f(t,x)没作任何连续性假定.     

非线性(k,n-k)共轭边值问题正解存在的特征值条件

该文在有关相应线性算子特征值的条件下,讨论非线性(k,n-k)共轭边值问题允许h(x)在x=0和x=1奇异．利用锥上的不动点指数理论获得了正解和多重正解的存在性．     

抽象空间中非线性算子方程变号解的存在性研究

利用Banach空间中的锥理论和不动点定理讨论了非线性算子方程变号解的存在性,给出了E_u_0空间下非线性算子方程变号解至少有一个变号解、一个正解和一个负解的条件,并讨论了仅通过一个上解条件得出非线性算子方程变号解的存在性定理.