On The Study Of Some Evolution Equations With Nonlocal Conditions

The thesis is concerned with two classes of problems:1) the Cauchy problems of a class of fractional evolution equations with nonlocal initial conditions,2) the Cauchy problems of a class of partial neutral evolution equations with nondensely defined operators and nonlocal initial conditions,The whole thesis is made up of four chapters.In Chapter 1 we present research background of this thesis and recent developments in the related problems.In Chapter 2, new criterions which allow us to relax the compactness and Lipschitz continuity on nonlocal item, ensuring the existence and uniqueness of mild solutions for the Cauchy problems of fractional evolution equations with nonlocal initial conditions, are established.Chapter 3 is concerned with the existence of mild solutions for partial neutral evolution equations with nondensely defined operators and nonlocal initial conditions in the case of nonlocal item being not Lipschitz and not compact.In the last Chapter, we present two applications to the abstract results in Chapter 2.