The present paper studied the dynamics of some multivalued random semiflow. The corresponding concept of random attractor for this case was introduced to study asymptotic behavior. The existence of random attractor of...The present paper studied the dynamics of some multivalued random semiflow. The corresponding concept of random attractor for this case was introduced to study asymptotic behavior. The existence of random attractor of multivalued random semiflow was proved under the assumption of pullback asymptotically upper semicompact, and this random attractor is random compact and invariant. Furthermore, if the system has ergodicity, then this random attractor is the limit set of a deterministic bounded set.展开更多
This paper obtains some fixed point theorems of semidifferentiable semicompact 1-set-contraction maps, which extend some known results in [1, 2, 4, 5, 7].
1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of ...1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow （random semiflow） under the assumption of the existence of compact absorbing set. In [3], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow and random semiflow under the assumptions of uniformly pullback asymptotically upper semicompact and closed graph. In [4], the authors consider the existence of pullback attractor of singlevalued nonautonomous semiflow and random semiflow under the assumption of pullback asymptotic compactness. Instead of these assumptions, we consider multivalued nonautonomous semiflow and multivalued random semiflow with weak pullback asymptotic upper semi-compactness and prove the existence of pullback attractors.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10571130)
文摘The present paper studied the dynamics of some multivalued random semiflow. The corresponding concept of random attractor for this case was introduced to study asymptotic behavior. The existence of random attractor of multivalued random semiflow was proved under the assumption of pullback asymptotically upper semicompact, and this random attractor is random compact and invariant. Furthermore, if the system has ergodicity, then this random attractor is the limit set of a deterministic bounded set.
文摘This paper obtains some fixed point theorems of semidifferentiable semicompact 1-set-contraction maps, which extend some known results in [1, 2, 4, 5, 7].
文摘1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow （random semiflow） under the assumption of the existence of compact absorbing set. In [3], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow and random semiflow under the assumptions of uniformly pullback asymptotically upper semicompact and closed graph. In [4], the authors consider the existence of pullback attractor of singlevalued nonautonomous semiflow and random semiflow under the assumption of pullback asymptotic compactness. Instead of these assumptions, we consider multivalued nonautonomous semiflow and multivalued random semiflow with weak pullback asymptotic upper semi-compactness and prove the existence of pullback attractors.
