共查询到20条相似文献,搜索用时 109 毫秒
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增算子的不动点和广义不动点 总被引:35,自引:2,他引:35
本文在紧性条件下证明了若干新的非连续的增算子的不动点定理.如果不假定增算子 A 满足连续性条件和紧性条件,我们证明了算子 A 有广义不动点. 相似文献
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In this paper,we give a fixed point theorem under the weak conditions and some corollaries,which generalize the results of [1]-[5]. 相似文献
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一个非连续增算子不动点定理及其应用 总被引:8,自引:0,他引:8
本文在无限区间上给出了一个新的非连续增算子不动点定理。作为应用,我们研究了无限区间上Banach空间中非线性积-微分方程初值问题解的存在性。 相似文献
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讨论了C[I,E]和L_p[I,E]中几类增算子,得到了若干新的不动点定理,并将其应用于证明非线性微分方程唯一解的存在性. 相似文献
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增算子的不动点定理及其对Banach空间含间断项的非线性方程的应用 总被引:16,自引:1,他引:16
设E是Banach空间,我们在空间C[I,E]中证明了增算子的某些新的不动点定理.本文完全没有使用人们普遍使用的连续性条件,并且用非常弱的逐点弱紧性条件代替了人们广泛使用的强紧性条件,从而统一并推广了许多已知结论.作为应用,我们研究了无穷维Banach空间上含间断项的非线性积分方程和微分方程最大解和最小解的存在性. 相似文献
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半序赋范空间及增算子的不动点定理 总被引:8,自引:1,他引:7
张宪 《应用泛函分析学报》2001,3(3):256-260
在赋范线性空间E中定义了由E上连续性泛函确定的半序,并由半序引出E上的锥,讨论了半序和锥的若干性质,最后证明了几个单调增算子的不动点定理。 相似文献
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In this paper, we study a class of nonlinear operator equations with more extensive conditions in ordered Banach spaces. By using the cone theory and Banach contraction mapping principle, the existence and uniqueness of solutions for such equations are investigated without demanding the existence of upper and lower solutions and compactness and continuity conditions. The results in this paper are applied to a class of abstract semilinear evolution equations with noncompact semigroup in Banach spaces and the initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces. The results obtained here improve and generalize many known results. 相似文献
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Valeri Obukhovskii 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1715-1728
We consider a semilinear functional differential inclusion with infinite delay and impulse characteristics in a Banach space assuming that its linear part is a non-densely defined Hille-Yosida operator. We assume that the multivalued nonlinearity of upper Carathèodory or almost lower semicontinuous type satisfies a regularity condition expressed in terms of the measures of noncompactness. We apply the theory of integrated semigroups and the theory of condensing multivalued maps to obtain local and global existence results. The application to an optimization problem for an impulsive feedback control system is given. 相似文献
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Valeri Obukhovskii Pietro Zecca 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(8):2765-2777
We introduce the notion of a multivalued causal operator and consider an abstract Cauchy problem in a Banach space for various classes of functional inclusions with causal operators. The methods of the topological degree theory for condensing maps are applied to obtain local and global existence results for this problem and to study the continuous dependence of a solution set on initial data. As application we generalize some existence results for semilinear functional differential inclusions and Volterra integro-differential inclusions with delay. 相似文献
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In this paper, we study the uniqueness and existence of fixed points of mixed monotone operators in the partially ordered Banach space. Our conclusions essentially improve the relevant results obtained by Liang and others. Moreover, as an application of our results, we prove the existence and uniqueness of a positive solution for a class of integral equations which cannot be solved by using previously available methods. 相似文献
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Zengqin Zhao 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1481-1490
In this paper, we introduce the e-concave-convex operator. Without any compact or continuous assumptions, we prove the existence and uniqueness of fixed points, giving monotone iterative sequences for the unique fixed point for the operator. Finally, we apply the results to an integral equation of polynomial type which possesses items of measurable functions. 相似文献
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In this paper we give the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions under the assumptions of the Hausdorff measure of noncompactness in separable and uniformly smooth Banach spaces. 相似文献
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Anthony To-Ming Lau Hiromichi Miyake Wataru Takahashi 《Nonlinear Analysis: Theory, Methods & Applications》2007
The purpose of this paper is to study iterative schemes of Browder and Halpern types for a semigroup of nonexpansive mappings on a compact convex subset of a smooth (and strictly convex) Banach space with respect to a sequence of strongly asymptotic invariant means defined on an appropriate space of bounded real valued functions of the semigroup. Various applications to the additive semigroup of nonnegative real numbers and commuting pairs of nonexpansive mappings are also presented. 相似文献
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In this paper we derive existence and comparison results for initial value problems in ordered Banach spaces. The considered problems can be implicit, singular, functional, discontinuous and nonlocal. The main tools are fixed point results in ordered spaces and theory of HL integrable vector-valued functions. Concrete examples are presented and solved. 相似文献
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This paper is concerned with nonlinear functional differential inclusions with infinite delay in Banach spaces. Using tools involving the measure of noncompactness and multi-valued fixed point theory, existence and continuous dependence results are obtained, for integral solutions, without the assumption of compactness on the associated nonlinear semigroup. 相似文献
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In this paper we derive the existence and comparison results for second order initial value problems in ordered Banach spaces. The considered problems can be implicit, singular, functional, discontinuous and nonlocal. The main tools are fixed point results in ordered spaces and the theory of locally HL integrable vector-valued functions. 相似文献