Several Problems About Equations In Abstract Spaces

Nonlinear functional analysis is an important branch of modern analysis mathematics. Itcan explain a lot of natural phenomena clearly, so more and more mathematical researchersare devoting their time to it. Among them,the nonlinear problem comes from a lot of branchesof applied mathematics and physics, it is at present one of the most active fields that is studiedin analytic mathematics.The present thesis mainly discusses the terminal value problems for integro-differentialequations in Banach spaces, the initial value problems for second order integro-differentialequations and two-point boundary value problems for second order integro-differentialequations, it consists four chapters．In chapter one, we mainly introduce background, research meaning and current situationsfo this study, and the main conclusions and motive of this thesis.In chapter two, we discuss the terminal value problems for integro-differential equationsin Banach spaces, by using monotone iterative technique and upper and lower solution. Itgeneralizes and improves the former corresponding results.In chapter three, we use monotone iterative technique and the cone theory to investigatethe existence of unique solutions of the initial value problems for second orderintegro-differential equations in Banach spaces.In chapter four, by using monotone iterative technique and upper and lower solution, weinvestigate wo-point boundary value problems for second order integro-differential equationsin Banach space. Our results improve and extend many recent results．...