Existence principles for differential equations and systems of equations

These lectures cover basic existence and sometimes uniqueness principles for systems of ordinary differential equations and for equations in Banach spaces. The existence principles are established by means of topological methods based on nonlinear alternatives for compact maps and for contractive maps. The initial analysis treats both classical and Caratheodory problems on compact intervals simultaneously and in a classical setting by recasting the boundary value problem as an equivalent integra-differential equation. Later problems with more general singularities and or unbounded intervals are treated.