Weighted Pseudo Almost Automorphy Of Differential Equations And Its Applications

This paper mainly discuss the properties of weighted pseudo almost automor-phic functions and related generalized functions. Applications of these functionsto various class of diferential equations are presented.The paper is composed of four chapters.In Chapter1, the historical background and recent developments of almostautomorphic functions and main results of this paper are introduced.In Chapter2, for linear boundary diferential equations, a Massera type cri-terion is established for the existence of an almost automorphic solution, whichextends the classical Massera periodic theorem on scalar periodic ordinary dif-ferential equations. On the other hand, for Li′enard equation, the relationshipsbetween bounded solution and the existence of almost automorphic solution areinvestigated, then using these results, we study the existence and uniqueness ofpseudo almost automorphic solutions of Li′enard equation.In Chapter3, by using the theory of Hille-Yosida operator and the Banachcontraction mapping principle, we investigate the weighted pseudo almost auto-moprhy for neutral abstract functional diferential equations with operator of nondense domain.In Chapter4, we systematically explore the properties of the weighted Stepanov-like pseudo almost automorphic functions in Banach space including completenessand translation invariance, establish the composition theorem for Stepanov-likepseudo almost automorphic functions. As an applications, we establish some suf-cient criteria for the existence, uniqueness of the weighted pseudo almost automor-phic solution to a class of neutral functional diferential equations, Volterra integralequations and semilinear fractional diferential equation.At the end of this paper, the remark of main findings and further study direc- tion are presented, many related references are listed.