Research On Qualitative Properties Of Solutions For Some Nonlinear Evolution Equations

This thesis is divided into two parts. The first part is devoted to the study of a class of abstract Cauchy problems for semilinear nonautonomous evolution equations involving nonlocal initial conditions. Combining the theory of evolution families and the fixed point theorem due to Krasnoselskii, as well as decomposition techniques, we prove the existence of the asymptotically periodic mild solutions to such problems.Our results generalize and improve some previous results since the(locally) Lipschitz continuity on the nonlinearity is not required. A partial differential equation is also presented as an application. The second part deals with the control problems of semilinear fractional delay evolution equations. Under rather mild conditions, we study the topological structure of solution sets(compactness and R?-property). Then,the information about the structure is employed to show the invariance of a reachability set of the control problem under nonlinear perturbations. An example is given to illustrate the feasibility of the abstract results.