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1.
In this paper,we obtain a general random fixed point theorem which generalizes the main results of Engle[4,7] and Bocsan[8]. The usefulness of this theorem seems to lie in the fact that unlike many random fixed point theorems obtained by using special methods[1,4,5-13] can be proved by using out general theorem (Theorem 1 and Corollaries 1 and 2). Finally,we indicate some possible applications of our results to nonlinear random integral and differential equations.  相似文献   

2.
In this paper, as the generalizations of Altman’s directional contractors[4,5] and Lee and Padgett’s random contractors[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.  相似文献   

3.
In this paper, first we show several new random fixed point theorems for random set-valued mappings and for a system of random set-valued mappings. Then, some applications of our results are given for the existence and uniqueness of random solution for a system of nonlinear random integral and differential equations. Our theorems improved and generalize many recent findings in [4–7, 9, 11–17].  相似文献   

4.
In this paper the fixed point index problem for a class of positive operators with boundary control conditions is discussed, and some sufficient conditions for the fixed point index to be equal to 1 or 0 are given. Moreover, a general fixed point theorem of expansions and compressions for cone is obtained, which generalizes and improves the corresponding results of [3,8,9]. As an application, we utilize the results presented above to study the existence conditions of positive solutions of nonlinear integral equations modelling infectious diseases.Project supported by National Natural Science Foundation of China.  相似文献   

5.
SOLUTIONSFORASYSTEMOFNONLINEARRANDOMINTEGRALANDDIFFERENTIALEQUATIONS¥DingXieping(丁协平)WangFan(王凡)(DepartmentofMathematics,Sich...  相似文献   

6.
This paper is the continuation of [1]. In this paper, we give another criteria of the existence of solutions for nonlinear random Volterra integral. A comparison theorem and the existence of random extremal solutions are also obtained by using the notion of ordering with respect to a cone. Our theorems generalize the corresponding results of Vaughan[2,3] and Lakshmikantham[4,5].  相似文献   

7.
Random fixed point theorems are of fundamental importance in probabilistic functional analysis. In complete separable metric space random fixed point theorems have been discussed by Bharucha-Reidf1/27, Hans[3], Itohf4,5J and the author’s papers[15-20].In this paper we obtain a random fixed point theorem for commuting random operators in probabilistic functional analysis. Our results generalize some important results also extend and unify some results in Jungck[6,7,8]t Das and Naiki[9] as well as Bhoades[10] adn ciric[11].  相似文献   

8.
I.IntroductionTheexistenceandcomparisonresultsofsolutionsfornonlinearVolterraintegralequationsinstrongtopologyofBanachspaceshavebeenobtainedbyVaughnI"'"],LakshmikanthamIl3]andLakshmikantham-Leela114l.TheexistenceresultsofweaksolutionsfortheCauchyproblemof…  相似文献   

9.
IntroductionItiswell_knownthatthebasiccharacteristicsofnonlinearintegralequationofVolterratypearefundamentallydifferentfromthatofHammersteintype:Hammersteinintegralequationhasafixedupperlimitofintegration.Thismeansthatasolutionmustalwaysbedefinedovere…  相似文献   

10.
In this paper, we prove several existence theorems of random solutions to nonlinear random Volterra integral equations under the weak topology of Banach spaces. Then, as applications, we obtain the existence theorems of weak random solutions to random differential equations. Existence of extremal random solutions and a random comparison theorem for these random equations are also obtained. Our theorems improve and extend the corresponding results in [4,5,10,11,12]. Projects supported by the Science Fund of the Chinese Academy of Sciences.  相似文献   

11.
In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR 2 has fixed point index 1. We also give a number of applications to differential equations. In particular, we deduce that a number of existence methods for producing periodic solutions of differential equations in the plane always produce unstable solutions.  相似文献   

12.
This paper presents mechanical quadrature methods (MQMs) for solving nonlinear boundary Helmholtz integral equations. The methods have high accuracy of order O(h 3) and low computation complexity. Moreover, the mechanical quadrature methods are simple without computing any singular integration. A nonlinear system is constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system are proved based on an asymptotical compact theory and the Stepleman theorem. Using the h 3-Richardson extrapolation algorithms (EAs), the accuracy to the order of O(h 5) is improved. To slove the nonlinear system, the Newton iteration is discussed extensively by using the Ostrowski fixed point theorem. The efficiency of the algorithms is illustrated by numerical examples.  相似文献   

13.
This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and thin set-valued Caristi’s fixed point theorem. The results stated in this paper improve and strengthen the corresponding results in [4].  相似文献   

14.
NEWVERSIONOFKKMTHEOREMINPROBABILISTICMETRICSPACESWITHAPPLICATIONSZhangShisheng(张石生)YeolJeCho(赵烈济)WuXiang(吴鲜)(ReceivedMay7,199...  相似文献   

15.
ONACLASSOFNEWKKMTHEOREMWITHAPPLICATIONSZhangShisheng(张石生),ZhangXian(张宪)(ReceivedMay15,1995)Abstract:Inthispaper,aclassofnewKK...  相似文献   

16.
In the present paper, we shall consider a nonlinear thermoconvection problem consisting of a coupled system of nonlinear partial differential equations due to temperature dependent coefficients. We prove that weak solutions exist in appropriate Sobolev spaces under mild hypothesis on the regularity of the data. This result is established through a fixed point theorem for multivalued functions, which requires a detailed analysis of the continuous dependence of auxiliary problems, including the associated Lagrange multipliers of the generalized Navier—Stokes system.  相似文献   

17.
Browder[1] obtained the sharpened forms of the Schauder fixed point theorem. Many authors generalized Browder’s results in several aspects. Recently, H.M. Ko and K.K. Tan[2,3] generalized Browder’s theorems to the coincidence theorems of set-valued mappings. In this paper, we also show some coincidence theorems oj set-valued mappings. They improve and generalize the important results in [1,2,3].  相似文献   

18.
The aim of this work is to give a direct and constructive proof of existence and uniqueness of a global solution to the equations of age-dependent population dynamics introduced and considered by M. E. Gurtin & R. C. MacCamy in [3]. The linear theory was developed by F. R. Sharpe & A. J. Lotka [10] and A. G. McKendrick [8] (see also [1], [9]) and extended to the nonlinear case by M. E. Gurtin & R. C. MacCamy in [3] (see also [4] [5] [6]). In [3], the key of the proof of existence and uniqueness was to reduce the problem to a pair of integral equations. In fact, as we shall see, the problem can also be solved by a simple fixed point argument. To outline more clearly the ideas of the proof, we will first discuss the setting and the resolution of the linear case, and then we will generalize the results of [3].  相似文献   

19.
As a continuation of a previous work on linearization of class C1 of diffeomorphisms and flows in infinite dimensions near a fixed point, in this work we deal with the case of a saddle point with some non-resonance restrictions for the linear part. Our result can be seen as an extension of results by Hartman [Boletin de la Sociedad Matematica Mexicana 5(2), 220–241 (1960)] and Aronson, Belitskii and Zhuzhoma [Introduction to the Qualitative Theory of Dynamical systems on surfaces, AMS Transl. Math. Monog. vol.153, pp. 268–277 (1996)] in dimension two. We also present an application to a system of nonlinear wave equations.AMS Subject Classifications: Primary: 35B05, 34G20. Secondary: 35B40, 34D05.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday  相似文献   

20.
IntroductionThestudiesofpositiveradialsolutionsforfollowingsemilinearellipticboundaryvalueproblem(P) Δu(X) +g( |X|)f(u(X) ) =0 ,  R1<|X|<R2 ,u(X) ||X| =R1 =u(X) ||X| =R2 =0(whereR1>0 ,X ∈Rn,n ≥ 2 )arebeingcontinuedforrecent 2 0yearswithoutinterruption[1- 11],becausetheproblem (P)haswi…  相似文献   

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