SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Stability analysis for impulsive stochastic fuzzy p-Laplace dynamic equations under Neumann or Dirichlet boundary condition

Ruofeng Rao1* and Zhilin Pu12

Author Affiliations

1 Institution of Mathematics, Yibin University, Yibin, Sichuan, 644007, P.R. China

2 College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan, 610066, P.R. China

For all author emails, please log on.

Boundary Value Problems 2013, 2013:133  doi:10.1186/1687-2770-2013-133

Published: 20 May 2013

Abstract

Under Neumann or Dirichlet boundary conditions, the stability of a class of delayed impulsive Markovian jumping stochastic fuzzy p-Laplace partial differential equations (PDEs) is considered. Thanks to some methods different from those of previous literature, the difficulties brought by fuzzy stochastic mathematical model and impulsive model have been overcome. By way of the Lyapunov-Krasovskii functional, Itô formula, Dynkin formula and a differential inequality, new LMI-based global stochastic exponential stability criteria for the above-mentioned PDEs are established. Some applications of the obtained results improve some existing results on neural networks. And some numerical examples are presented to illustrate the effectiveness of the proposed method due to the significant improvement in the allowable upper bounds of time delays.

MSC: 34D20, 34D23, 34B45, 34B37, 34K20.

Keywords:
differential inequality; Laplace diffusion; Markovian jumping