International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2557

Full Length Research Paper

Existence of solutions for G-SDEs with upper and lower solutions in the reverse order

Faiz FaizUllah1* and Daxiong Piao2    
1College of Physical and Environmental Oceanography, Ocean University of China, Qingdao 266100, PR China. 2School of Mathematical Sciences, Ocean University of China, Qingdao 266100, PR China.     
Email: [email protected]

  •  Accepted: 16 December 2011
  •  Published: 16 January 2012

Abstract

The existence of solutions for stochastic differential equations under G-Brownian motion (G-SDEs) of the typein the presence of a lower solution  and an upper solution  in a reverse order is established. By the method of upper and lower solutions in the reverse order, it is shown that the G-SDEs have more than one solution if the drift coefficients are discontinuous functions.

 

Key words: Upper and lower solutions in reverse order, stochastic differential equations, G-Brownian motion, discontinuous drift coefficient, existence.