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1.
一类种群系统的适定性及最优收获问题   总被引:11,自引:0,他引:11  
本文研究了一类非线性时变种群扩散系统的适定性及最优收获问题.利用压缩不 动点原理讨论了该种群系统的解的存在唯一性.证明了最优收获控制的存在性,并且获 得了最优控制的唯一性和所满足的必要条件.  相似文献
2.
This paper deals with the asymptotic theory of initial value problems for semilinear waveequations in three space dimensions. The well-posedness and validity of formal approximations ona long time scale of order |ε|^-1 are discussed in the classical sense of C^2 This result describes aceu-ratively the approximations of solutions. At the end of this paper an application of the asymptotictheory is given to analyze a special model for a perturbed wave equation,  相似文献
3.
Well-posedness and convexity in vector optimization   总被引:9,自引:0,他引:9  
We study a notion of well-posedness in vector optimization through the behaviour of minimizing sequences of sets, defined in terms of Hausdorff set-convergence. We show that the notion of strict efficiency is related to the notion of well-posedness. Using the obtained results we identify a class of well-posed vector optimization problems: the convex problems with compact efficient frontiers.  相似文献
4.
Well-Posedness and Scalarization in Vector Optimization   总被引:8,自引:0,他引:8  
In this paper, we study several existing notions of well- posedness for vector optimization problems. We separate them into two classes and we establish the hierarchical structure of their relationships. Moreover, we relate vector well-posedness and well-posedness of an appropriate scalarization. This approach allows us to show that, under some compactness assumption, quasiconvex problems are well posed.The authors thank Professor C. Zălinescu for pointing out some inaccuracies in Ref. 11. His remarks allowed the authors to improve the present work.  相似文献
5.
Banach空间中关于有界集的同时远达问题的适定性   总被引:7,自引:1,他引:6       下载免费PDF全文
倪仁兴  李冲 《数学学报》1999,42(5):823-826
本文研究Banach空间中关于有界集的同时远达问题的适定性,在集合的Hausdorff距离下,证明了:对自反局部一致凸Banach空间中的闭有界集K,使所有关于K的同时远达问题是适定的紧凸子集A全体在紧凸子集全体中是Gδ型集.  相似文献
6.
7.
非静力旋转流体方程初值问题的适定性   总被引:4,自引:1,他引:3  
应用分层理论所提供的方法,通过对非静力旋转流体方程这个数学模型本身的拓扑性质进行系统的理论分析和研究,来讨论对于这个方程的初值问题的几种不同提法以及相应的适定性问题。  相似文献
8.
On the Tikhonov Well-Posedness of Concave Games and Cournot Oligopoly Games   总被引:4,自引:0,他引:4  
The purpose of this paper is to investigate whether theorems known to guarantee the existence and uniqueness of Nash equilibria, provide also sufficient conditions for the Tikhonov well-posedness (T-wp). We consider several hypotheses that ensure the existence and uniqueness of a Nash equilibrium (NE), such as strong positivity of the Jacobian of the utility function derivatives (Ref. 1), pseudoconcavity, and strict diagonal dominance of the Jacobian of the best reply functions in implicit form (Ref. 2). The aforesaid assumptions imply the existence and uniqueness of NE. We show that the hypotheses in Ref. 2 guarantee also the T-wp property of the Nash equilibrium.As far as the hypotheses in Ref. 1 are concerned, the result is true for quadratic games and zero-sum games. A standard way to prove the T-wp property is to show that the sets of -equilibria are compact. This last approach is used to demonstrate directly the T-wp property for the Cournot oligopoly model given in Ref. 3. The compactness of -equilibria is related also to the condition that the best reply surfaces do not approach each other near infinity.  相似文献
9.
Unified Approaches to Well-Posedness with Some Applications   总被引:3,自引:0,他引:3  
We present unified approaches to Hadamard and Tykhonov well-posedness. As applications, we deduce Tykhonov well- posedness for optimization problems, Nash equilibrium point problems and fixed point problems etc. Especially, by applying such approaches, we deal with the well- posedness as stated in (Lignola and Morgan (2000), Journal of Global Optimization 16, 57–67) in which Lignola and Morgan investigated directly and intensively Tykhonov types of well- posedness for optimization problems with constraints defined by variational inequalities, namely, generalized well- posedness and strong well- posedness. We give some sufficient conditions for Hadamard well- posedness of such problems and deduce relations between Hadamard type and Tykhonov type of well- posedness. Finally, as corollaries, we derive generalized well- posedness and strong well- posedness for these problems.  相似文献
10.
Well-Posedness by Perturbations of Variational Problems   总被引:3,自引:0,他引:3  
In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.  相似文献
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