非线性随机积分和微分方程组的解*
Solutions for a System of Nonlinear Random Integral and Differential Equations
-
摘要: 在本文中我们首先对具有随机定义域的连续随机算子组证明了Darbao型不动点定理。应用此定理我们给出了非线性随机Volterra积分方程组和非线性随机微分方程组的Cauchy问题解的存在性准则。这些随机方程组的极值随机解的存在性和随机比较结果也被获得。我们的定理改进和推广Tyaughn,Lakshmikantham,Lakshmikantham-Leela,DeBlast-Myjak和第一作者的相应结果。
-
关键词:
- 非线性积分方程 /
- 随机Volterra积分方程 /
- 随机Cauchy问题 /
- 极值随机解 /
- 比较结果
Abstract: In this paper we first prove a Darbao type fixed point theorem for a system of continuous random operators with random domains. Thenb, by using the theorem. wegive the existence criteria of solutions for a systems of nonlinear random volterraintegral equations and for the Cauchy problem of a system of nonlinear random differential equations. The existence of extremal random solutions and random comparison results for these systems of random equations are also obtained our theorems improve and generalize the corresponding results of Vaughn Lakshmikantham Lakshmidantham-Leela De blasi-Myjak and Ding. -
[1] A. T. Bharucha-Reid, Random Integal Equations. Acad. Press, New York(1972). [2] V. Lakshmikantam and S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, New York(1981). [3] C. J. Tsokos and W. J. Padgetl, Random Intebral Equations with Applications to Life Science and Engineering, Acad, Press. New York(1974). [4] 丁协平,随机积分和微分方程解的存在性准则,应用数学和力学.6(3) (1985), 265-270. [5] 丁协平,随机积分方程和微分方程解的存在性和比较结果,应用数学和力学.7(7) (1986),597-604. [6] R. L. Vaughn, Existence arid comparison results for nonlinear Volterra integral equations in Banach spaces, Appl. Anal. 7(1978), 337-348. [7] R. C. Vaughn, Criteria for the existence and comparison of solutions to nonlinear Volterra integral equations in Banaeh spaces, Nonlinear Equations in Abstract Sppaces, Acad. Press, New York(1978), 463-468. [8] V. Lakshmikantham, Existence and comparison results for Volterra integral equations,V. Lakshmikantham, Existence and comparison results for Volterra integal equations, Volterral Integal Equations, Springer-Verlag, 737(1979), 120-126. [9] F. S. De Blasi and J. Myjak, Random differential equations on closed subsets of Banach spaces, J. Mark. Anal. Appl. 90(1982), 273-285. [10] 丁协平,随机集值映射的不动点定理及其应用,应用数学和力学,5(4) (1984), 561-575.
点击查看大图
计量
- 文章访问数: 2015
- HTML全文浏览量: 48
- PDF下载量: 528
- 被引次数: 0