Criteria for the Existence of Solutions to Random Integral and Differential Equations

Ding Xie-ping

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1985 > 6(3): 265-270

Ding Xie-ping. Criteria for the Existence of Solutions to Random Integral and Differential Equations[J]. Applied Mathematics and Mechanics, 1985, 6(3): 265-270.

Citation:

Ding Xie-ping. Criteria for the Existence of Solutions to Random Integral and Differential Equations[J]. Applied Mathematics and Mechanics, 1985, 6(3): 265-270.

Citation:

Ding Xie-ping. Criteria for the Existence of Solutions to Random Integral and Differential Equations[J]. Applied Mathematics and Mechanics, 1985, 6(3): 265-270.

PDF( 421 KB)

Criteria for the Existence of Solutions to Random Integral and Differential Equations

Ding Xie-ping

Sichuan Teacher's College, Chengdu

Received Date: 1984-01-24
Publish Date: 1985-03-15

Abstract

Abstract

In [1], we proved a general rondom fixed point theorem and gave some applications. In this paper, we shall give further applications of the theorem. We first obtain a rondom Darbo's fixed point theorem, using the theorem, we give the criteria for the existence of solutions under compactness hypotheses to nonlinear rondom volterra integral equations and the Cauchy problem of nonlinear rondom differential equations. Our theorems improve andgeneralize some main results of Lakshmikanthem^[2], Vaughn^[3,4] as well as De Blasi and Myjak^[5].

FullText(HTML)

References(14)

References

[1]	丁协平,一般随机不动点定理及其应用,应用数学和力学,5,5(1984),699-708
[2]	Lakshmikantham V.,In Volterra Integral Equations,Springer-Verlag,737(1979),120-126.
[3]	Vaughn,R.L.,Existence and comparison results for nonlinear Volterra integnal equations in a Banach space,Appl.Analysis,7(1978),337-348.
[4]	Vaughn.R.L.,In Nonlinear Equations in Abstract Spaces,Academic Press,New York(1978),463-468.
[5]	De Blasi,F.S.and J.Myjak,Random differential equations on closed subsets of a Banach space,J.Math.Anal.Appl.90(1982),273-285.
[6]	Bharucha-Reid,A.T.,Random Integral Equations,Academic Press,New York(1972).
[7]	Tsokos,C.J and W.J.Padgett,Random Integral Equations with Applications to Life Sciences and Engineering,Academic Press,New York(1974).
[8]	Engl,H.W.A general stochastic fixed-point theorem for continuous random operators on stochastic domains,J.Math.Anal.Appl.,66(1978).220-231.
[9]	Engl,H.W.Random fixed point theorems,in Nonlinear Equations in Abstract Spaces.Academic Press,New York,(1978),67-80.
[10]	Bocsan,Gh.,A general random fixed point theorem and application to random equations,Rev.Roum.Math.Pures et.Appl.,26(3)(1981),375-379.
[11]	Himmelberg C.J.,Measurable relations,Fund Math.87(1975),53-72.
[12]	Castaing,C.and M.Valadier.,Convex Analysis and Measurable Multifunctions,Springer-Verlag 580(1977).
[13]	Lakshmikantham,V.and S.Leela,Nonlinear Differential Equations in Abstract Spaces.Pergamon Press,New York(1981).
[14]	Rus I.A.,On a theoremof Eisenfeld-Lakshmikantham,Nonlinear Anal.,TMA.,7(3)(1983),279-281.