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Asymptotic behavior of stochastic p-Laplacian-type equation with multiplicative noise

Wenqiang Zhao

Author Affiliations

School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

Boundary Value Problems 2012, 2012:61  doi:10.1186/1687-2770-2012-61

Published: 22 June 2012


The unique existence of solutions to stochastic p-Laplacian-type equation with forced term satisfying some growth and dissipative conditions is established for the initial value in <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/61/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/61/mathml/M1">View MathML</a>. The generation of a continuous random dynamical system and the existence of a random attractor for stochastic p-Laplacian-type equation driven by multiplicative noise are obtained. Furthermore, we obtain a random attractor consisting of a single point and thus the system possesses a unique stationary solution.

MSC: 60H15, 35B40, 35B41.

random dynamical systems; stochastic p-Laplacian-type equation; random attractors