Solutions of the Schrödinger equation in a Hilbert space

Abstract

Necessary and sufficient conditions for the existence of a solution of a boundary-value problem for the Schrödinger equation are obtained in the linear and nonlinear cases. Analytic solutions are represented using the generalized Green operator.

Bifurcation of solutions of the second order boundary value problems in Hilbert spaces

“…Remark 2. Proposed theory gives possibility to investigate branching of solutions of boundary value problem (3.1) (see [5], [4]).…”

Bifurcation of solutions of the second order boundary value problems in the Hilbert spaces

“…Let x 1 (t) = y 0 (t), x 2 (t) = y ′ 0 (t), x(t) = (x 1 (t), x 2 (t)) T , then we can rewrite boundary value problem (3) in the form of the operator system x ′ 0 (t) = B(t)x 0 (t) + g(t), lx 0 (•) = α,…”