We provide a systematic study of boundary data maps, that is, 2 × 2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with one-dimensional Schrödinger operators on a compact interval [0, R] with separated boundary conditions at 0 and R. Most of our results are formulated in the non-self-adjoint context. Our principal results include explicit representations of these boundary data maps in terms of the resolvent...

In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem $$ϵy^{\text{'}\text{'}}+ky=f(t,y),t\in \langle a,b\rangle ,k<0,0<ϵ\ll 1$$ satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations.