Existence Of Generation Element Of The Nonliear Semigroups Of The Lipschitz-α Opearator

Hille and Yosida proved the generation theorem of C₀ semigroups firstly, but the course of study of a nonlinear semigroups is very slow. This paper is concerned with the problem of a nonlinear semigroup of Lipschitz-αoperator, based on the nonlinear semigroup of Lipschitz operator. This new semigroup extende the nonlinear semigroup of Lipschitz operator. In this paper, new theorems of the generation of the nonlinear semigroup of Lipschhitz-αoperator are established.This paper consists of three chapters. The main contents are the following:In the first chapter, we recall the development of the semigroups. Then we introduce the meaning of doing research on the nonlinear semigroups of Lipschitz -αoperator.In the second chapter, we present some mathematical preliminaries. These include the theorems in normed spaces, operator theory and operator semigroup. In the third chapter, we established the new theory of the nonlinear semigroup of the Lipschitz-αoperator.