Electron. J. Diff. Equ., Vol. 2012 (2012), No. 235, pp. 1-9.

Solutions to fourth-order random differential equations with periodic boundary conditions

Xiaoling Han, Xuan Ma, Guowei Dai

Abstract:
Existence of solutions and of extremal random solutions are proved for periodic boundary-value problems of fourth-order ordinary random differential equations. Our investigation is done in the space of continuous real-valued functions defined on closed and bounded intervals. Also we study the applications of the random version of a nonlinear alternative of Leray-Schauder type and an algebraic random fixed point theorem by Dhage.

Submitted October 17, 2012. Published December 21, 2012.
Math Subject Classifications: 47H40, 47N20, 60H25.
Key Words: Random differential equation; periodic boundary conditions; random solution; extremal solutions.

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Xiaoling Han
Department of Mathematics
Northwest Normal University
Lanzhou, 730070, China
email: hanxiaoling@nwnu.edu.cn
  Xuan Ma
Department of Mathematics
Northwest Normal University
Lanzhou, 730070, China
email: sfsolo@163.com
Guowei Dai
Department of Mathematics
Northwest Normal University
Lanzhou, 730070, China
email: daiguowei@nwnu.edu.cn

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