| In this dissertation,we main study the existence of solutions for four kinds of differential systems,including:Chapter 1:The research background,the present situation and the main work of this dissertation are introduced from three aspects of impulsive differ-ential system,p-Laplacian operator and pseudo almost periodic function.Chapter 2:We study the existence of periodic solutions for a class impul-sive differential systems with a p-Laplacian operator and a parameter λ.By employing an existing critical point theorem,we find the range of the control parameter in which the p-Laplacian problem admits at least one non-zero weak periodic solution.Our results have extended some of the existing conclusions.Chapter 3:By employing the variational method and the least action prin-ciple,we study the existence of the nonzero periodic solution for Hamiltonian system with p-Laplacian operator and its perturbation system.Our results have extended some of the existing conclusions.Chapter 4:We study the existence and exponential stability of positive almost periodic solution of a nonlinear delay differential equation with impul-sive effects.We obtain the sufficient conditions for existence and exponential stability of positive almost periodic solution by using the contraction mapping principle as well as applying Gronwall-Bellman’s inequality.Chapter 5:By employing the fixed point theorem,we discuss a class of impulsive hematopoietic model,and come up with the sufficient conditions for the existence and exponential stability of pseudo almost periodic solutions.All the results mentioned above are newly found. |
