Variational Stability For Measure Differential Systems

In this dissertation,by using the theories of Kurzweil integral and generalized ordinary differential equations,we define notions of the variational stability and the variational-asymptotically stability for a kind of measure differential equations as follows Dx =F(x,t)+ g(x,t)Du and we discuss the variational stability and the variational-asymptotically stabili-ty for measure differential equations by using of the equivalent relationship of the measure differential equations and generalized ordinary differential equations.More-over,we define notions of the variational stability and the variational-asymptotically stability for a kind of measure functional differential equations as follows Dx = f(xt,t)Dg and we discuss the variational stability and the variational-asymptotically stability for measure functional differential equations by using the equivalent relationship of the measure functional differential equations and generalized ordinary differential equations.