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1.
给出了Banach空间的一个增算子不动点定理,将这一定理应用到Banach空间的积分-微分方程,给出了一类积分-微分方程的连续可微最大解和连续可微最小解的存在性定理.  相似文献   

2.
王信峰 《应用数学》2007,20(2):239-242
利用单调迭代技术,本文首先讨论了Banach空间一阶脉冲积分-微分方程初值问题最大解与最小解的存在性.在此基础上,讨论了右端项中带有一阶导数的二阶脉冲积分-微分方程初值问题最大解与最小解的存在性.最后的例子说明对导数的限制条件是可验证的.  相似文献   

3.
研究一类高阶积分微分方程的周期边值问题,利用上下解和单调迭代法证得最大解和最小解的存在性。  相似文献   

4.
证明了Banach空间上一类非连续的弱紧增算子的不动点定理,特别获得了最大不动点与最小不动点的存在性,改进了已有的某些结果.作为应用,讨论了Banach空间中含间断项的常微分方程初值问题最大解与最小解的存在性.  相似文献   

5.
增算子不动点的迭代求法及其应用   总被引:6,自引:1,他引:5  
张金清  孙经先 《应用数学》2005,18(1):128-135
设E是Banach空间 ,本文在空间C[I,E]中得到了若干新的增算子不动点的存在性定理及其不动点的迭代求法 .作为应用 ,我们研究了Banach空间上非线性积分方程最大解和最小解及其单调迭代方法  相似文献   

6.
本文讨论了Banach空间含间断项的一阶混合型脉冲微分-积分方程的周期边值问题,通过建立一个比较定理,应用不动点定理与上、下解方法证明了最大解、最小解及迭代解的存在性,推广改进了某些文献中的相应结果。  相似文献   

7.
本文讨论了Banach空间含间断项的一类二阶非线性脉冲微分方程终值问题,应用不动点定理与上下解方法,获得了其最大解和最小解的存在性.  相似文献   

8.
第一部分,介绍分数阶导数的定义和著名的Mittag—Leffler函数的性质.第二部分,利用单调迭代方法给出了具有2序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性和唯一性.第三部分,利用上下解方法和Schauder不动点定理给出了具有2序列Riemann—Liouville分数阶导数微分方程周期边值问题解的存在性.第四部分,利用Leray—Schauder不动点定理和Banach压缩映像原理建立了具有n序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性、唯一性和解对初值的连续依赖性.第五部分,利用锥上的不动点定理给出了具有Caputo分数阶导数微分方程边值问题,在超线性(次线性)条件下C310,11正解存在的充分必要条件.最后一部分,通过建立比较定理和利用单调迭代方法给出了具有Caputo分数阶导数脉冲微分方程周期边值问题最大解和最小解的存在性.  相似文献   

9.
单调迭代法与一阶脉冲泛函微分方程周期边值问题   总被引:6,自引:0,他引:6  
何智敏  葛渭高 《数学学报》2005,48(1):171-176
本文利用单调迭代法与上下解方法,研究了一阶脉冲泛函做分方程周期边值问题最大解与最小解的存在性.  相似文献   

10.
孙经先 《数学学报》1991,34(5):665-674
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   

11.
孙经先  张晓燕 《数学学报》2005,48(3):439-446
从应用问题的需要出发,给出了一类新的算子-凸幂凝聚算子的定义,推广了凝聚算子的概念,并证明了这类新算子的不动点定理,从而推广了著名的Schauder不动点定理和Sadovskii不动点定理.作为应用,获得了Banach空间中一类具有非紧半群的半线性发展方程初值问题整体mild解和正mild解的存在性.  相似文献   

12.
胡适耕 《应用数学》1994,7(3):269-274
本文考虑Banach空间中形如x″=A(t)x f(t,x,x′)的2阶微分方程,利用基于度理论的一定不动点定理得到了以上方程存在周期解的若干充分条件。  相似文献   

13.
In this paper, we establish the existence of three periodic positive solutions for a class of abstract integral equations by Leggett-Williams fixed point theorem. Using the existence results for abstract integral equations, the population models are also considered.  相似文献   

14.
In this paper, we prove that the space is complete. This not only gives an affirmative answer to a basic problem in this field, but also enables us to obtain an existence and uniqueness theorem of pseudo almost automorphic mild solutions to semilinear differential equations in Banach spaces. An example is given to illustrate our theorem. The work was supported partly by the National Natural Science Foundation of China, the NCET-04-0572 and Research Fund for the Key Program of the Chinese Academy of Sciences.  相似文献   

15.
We introduce a new extension of the classical Leray-Schauder topological degree in a real separable reflexive Banach space. The new class of mappings for which the degree will be constructed is obtained essentially by replacing the compact perturbation by a composition of mappings of monotone type. It turns out that the class contains the Leray-Schauder type maps as a proper subclass. The new class is not convex thus preventing the free application of affine homotopies. However, there exists a large class of admissible homotopies including subclass of affine ones so that the degree can be effectively used. We shall construct the degree and prove that it is unique. We shall generalize the Borsuk theorem of the degree for odd mappings and show that the ‘principle of omitted rays’ remains valid. To illuminate the use of the new degree we shall briefly consider the solvability of abstract Hammerstein type equations and variational inequalities.  相似文献   

16.
In this paper, an existence result for perturbed abstract measure differential equations is proved via hybrid fixed point theorems of Dhage [B.C. Dhage, On some nonlinear alternatives of Leray-Schauder type and functional integral equations, Arch. Math. (Brno) 42 (2006) 11-23] under the mixed generalized Lipschitz and Carathéodory conditions. The existence of the extremal solutions is also proved under certain monotonicity conditions and using a hybrid fixed point theorem of Dhage given in the above-mentioned reference, on ordered Banach spaces. Our existence results include the existence results of Sharma [R.R. Sharma, An abstract measure differential equation, Proc. Amer. Math. Soc. 32 (1972) 503-510], Joshi [S.R. Joshi, A system of abstract measure delay differential equations, J. Math. Phy. Sci. 13 (1979) 497-506] and Shendge and Joshi [G.R. Shendge, S.R. Joshi, Abstract measure differential inequalities and applications, Acta Math. Hung. 41 (1983) 53-54] as special cases under weaker continuity condition.  相似文献   

17.
The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called “intersection” theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. Math. 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.  相似文献   

18.
In this paper, we generalize Stein?s method to “infinite-variate” normal approximation that is an infinite-dimensional approximation by abstract Wiener measures on a real separable Banach space. We first establish a Stein?s identity for abstract Wiener measures and solve the corresponding Stein?s equation. Then we will present a Gaussian approximation theorem using exchangeable pairs in an infinite-variate context. As an application, we will derive an explicit error bound of Gaussian approximation to the distribution of a sum of independent and identically distributed Banach space-valued random variables based on a Lindeberg-Lévy type limit theorem. In addition, an analogous of Berry-Esséen type estimate for abstract Wiener measures will be obtained.  相似文献   

19.
We give a parametrization with perfect subsets of 2 of the abstract Ellentuck theorem (see [T.J. Carlson, S.G. Simpson, Topological Ramsey Theory, in: J. Ne?etrˆil, V. Rödl (Eds.), Mathematics of Ramsey Theory, Algorithms and Combinatorics, vol. 5, Springer, Berlin, 1990, pp. 172-183], [S. Todorcevic, Introduction to Ramsey spaces, to appear] or [S. Todorcevic, Lecture notes from a course given at the Fields Institute in Toronto, Canada, Autumn 2002]). The main tool for achieving this goal is a sort of parametrization of an abstract version of the Nash-Williams theorem. As corollaries, we obtain some known classical results like the parametrized version of the Galvin-Prikry theorem due to Miller and Todorcevic [A.W. Miller, Infinite combinatorics and definability, Ann. Pure Appl. Logic 41 (1989) 179-203], and the parametrized version of Ellentuck's theorem due to Pawlikowski [Parametrized Ellentuck theorem, Topology Appl. 37 (1990) 65-73]. Also, we obtain parametized vesions of nonclassical results such as Milliken's theorem [K.R. Milliken, Ramsey's theorem with sums or unions, J. Combin. Theory (A) 18 (1975) 276-290], and we prove that the family of perfectly Ramsey subsets of is closed under the Souslin operation.  相似文献   

20.
In this paper, a new approach is provided to study the asymptotic behavior of functions. A Tauberian theorem is improved and applied to describe the asymptotic behavior of abstract functional differential equations of the form
  相似文献   

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