In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy~ and the results also hold for some nonlinear equations with the form ...In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy~ and the results also hold for some nonlinear equations with the form x＇（t） = f（t,x（t）） ＋ λg（t,x（t））, where f,g are pseudo-almost automorphic functions. We prove our main result by the application of Leray-Schauder fixed point theorem.展开更多
Almost automorphic is a particular case of the recurrent motion, which has been studied in differential equations for a long time. We introduce square-mean pseudo almost automorphic and some of its properties, and the...Almost automorphic is a particular case of the recurrent motion, which has been studied in differential equations for a long time. We introduce square-mean pseudo almost automorphic and some of its properties, and then study the pseudo almost automorphic solution in the distribution sense to stochastic differential equation driven by Levy process.展开更多
In this paper, we consider a semilinear difference equation in a Banach space. Under some suitable conditions on f, we prove the existence and uniqueness of a weighted pseudo almost automorphic sequence solution to th...In this paper, we consider a semilinear difference equation in a Banach space. Under some suitable conditions on f, we prove the existence and uniqueness of a weighted pseudo almost automorphic sequence solution to the equation.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11126070 and 11201309the Natural Science Foundation of SZU(201111)+1 种基金supported the National Natural Science Foundation of China under Grant No.11026168 and 11201046the Fundamental Research Funds for the Central Universities in China(DUT12LK32,DUT13JS02)
文摘In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy~ and the results also hold for some nonlinear equations with the form x＇（t） = f（t,x（t）） ＋ λg（t,x（t））, where f,g are pseudo-almost automorphic functions. We prove our main result by the application of Leray-Schauder fixed point theorem.
基金The authors are grateful to the anonymous referees for very helpful comments on the original version of this paper. The work of Xinwei FENG was partially supported by the National Natural Science Foundation of China （Grant No. 11601280）. The work of Gaofeng ZONG was supported in part by the National Natural Science Foundation of China （Grant Nos. 11501325, 11231005） and the China Postdoctoral Science Foundation （Grant No. 2018T110706）.
文摘Almost automorphic is a particular case of the recurrent motion, which has been studied in differential equations for a long time. We introduce square-mean pseudo almost automorphic and some of its properties, and then study the pseudo almost automorphic solution in the distribution sense to stochastic differential equation driven by Levy process.
基金Supported by the National Science Foundation of China(11201109)the National Science Research Project of Anhui Educational Department(KJ2012Z335)the Foundations for Talents of Hefei Normal University(2014136KJB01,2014136KJC04)
基金supported by Tianyuan Youth Foundations for Mathematics of NSFC (Grant No.11026150, 11026098)the Doctor Scientific Research Foundation of Shandong Institute of Business and Technology (Grant No.521-014-306131)
文摘In this paper, we consider a semilinear difference equation in a Banach space. Under some suitable conditions on f, we prove the existence and uniqueness of a weighted pseudo almost automorphic sequence solution to the equation.
