Article citationsMore>>

Kostyuchenko, A.G. and Shkalikov, A.A. (1983) Selfadjoint Quadratic Operator Pencils and Elliptic Problem. Functional Analysis and Its Applications, 17, 109-128.
http://dx.doi.org/10.1007/BF01083136

has been cited by the following article:

• TITLE: Integral Representations for the Solutions of the Generalized Schroedinger Equation in a Finite Interval

  AUTHORS: Anar Adiloglu Nabiev, Rauf Kh. Amirov

  KEYWORDS: One Dimensional Schroedinger Equation, Fundamental Solutions, Transformation Operator, Inte-gral Representation, Differential Equation with Discontinues Coefficient, Kernel of an Integral Op-erator, Integral Equation, Method of Successive Approximations

  JOURNAL NAME: Advances in Pure Mathematics, Vol.5 No.13, November 17, 2015

  ABSTRACT: We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.