Applied Mathematics and Mechanics (English Edition) ›› 1985, Vol. 6 ›› Issue (3): 269-275.

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CRITERIA FOR THE EXISTENCE OF SOLUTIONS TO RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS

Ding Xie-ping   

  1. Sichuan Teacher’s College, Chengdu
  • Received:1984-06-24 Online:1985-03-18 Published:1985-03-18

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].

Key words: fractional differential form, Cartesian coordinate, spherical coordinate, cylindrical coordinate

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