Boundary value problems for systems of differential equations

Abstract

We give sufficient conditions for systems of the form y′ = f(x, y), x in [0, 1] and y″ = f(x, y, y′), x in [0, 1] to have solutions y with (x, y) in Ω ⊆ [0, 1] x Rn. We use degree theory and allow the shape of Ω to depend on x.