Existence theory for ordinary differential equations on compact and noncompact intervals

Abstract

This chapter presents existence results for second order differential equations on finite, semi-finite, infinite, open and half open intervals. In particular, we examine the problem $$y'' = f(t,y,y'){\text{ }}a.e.{\text{ }}on{\text{ }}(a,b)$$ (1.1) where −∞ ≤ a ≤ b ∞ and f is a locally Caratheodory function. We also discuss seperately the problem (1.1) with boundary conditions: $$ y(a) = c $$ (1.2) , and/or $$ y(b) = d $$ (1.3) .