Existence And Asymptotic Stability Of Solutions For The Vibration Equations Of Beam With Structural Damping

In Banach spaces,by using operator semigroup theory,fixed point theorem,the existence of mild solutions for the Semilinear vibration equation of beam with structural damping is studied,and the existence and asymptotic stability of mild ?-periodic solutions for linear and Semilinear vibration equations of beam is discussed.The main results of this paper are as follows:In Chapter 1,we introduce the research background for vibration equation of beam with structural damping,the main work of this paper,some preliminaries on operator semigroups theory and noncompactness measure.The second Chapter gives the fixed point theorem of convex-power condensing operator,By using the fixed point theorem of convex-power condensing operator,under the noncompactness measure,the existence of global mild solutions and positive mild solutions for the initial value problem is obtained as the associated semigroups are equicontinuous.In Chapter 3,First of all,the existence and asymptotic stability of mild ?-periodic solutions is discussed and obtain the mild ?-periodic solutions with semigroup for linear vibration equation of beam with structural damping.Secondly,in the Lipschitz perturbation case,using the estimation of periodic solutions for linear vibration equation of beam,obtained existence and asymptotic stability of periodic solutions for the semilinear vibration equation of beam.