| Integro-differential equations are widely applied to the mathematical modeling of prac-tical problems from physics,biomedicine,economy and ecology.In this thesis,combined with fundamental theories and techniques of integro-differential equations and functional analysis,we mainly investigate the solvability and controllability of some evolution integro-differential systems with nonlocal initial conditions.The main contents are focused upon the solvability and approximate controllability of time-varying integro-differential inclu-sion with Clarke sub-differential,solvability and topological properties on solution sets of stochastic evolution integro-differential inclusions with Poisson jumps when the resolvent operator is compact or non-compact,and solvability of semi-linear integro-differential vari-ational inequalities when the resolvent operator is compact or non-compact.The thesis consists of six chapters.In this first chapter,we briefly introduce the background,advance of concerned topics,and the sketch of this thesis.The second chapter is concerned with some preliminary results of function spaces,re-solvent operators,measure of noncompactness,R_δ-set,multivalued analysis,variational in-equalities,and some other theorems and lemmas needed in this thesis.In the third chapter,we mainly consider the solvability and approximate controllability of time-varying integro-differential inclusion with Clarke sub-differential and a non-local initial condition.In the fourth chapter,we mainly investigate the solvability and topological properties of solution set for stochastic evolution integro-differential inclusions with Poisson jumps when the resolvent operator is compact or non-compact,respectively.In the fifth chapter,we mainly consider the solvability of semi-linear integro-differential variational inequalities with non-local initial conditions when the resolvent operator is com-pact or non-compact,respectively.Finally,in the sixth chapter we give summaries and other problems to be further investi-gated in the future. |
