Article citationsMore>>

B. Curgus and T. T. Read, “Discreteness of the Spectrum of Second-Order Differential Operators and Associated Embedding Theorems,” Journal of Differential Equations, Vol. 184, No. 2, 2002, pp. 526-548. doi:10.1006/jdeq.2001.4152

has been cited by the following article:

• TITLE: Cyclic Operator Decomposition for Solving the Differential Equations

  AUTHORS: Ivan Gonoskov

  KEYWORDS: Operator Decomposition; Spectral Theory; Propagator

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.1A, January 30, 2013

  ABSTRACT: We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the generating function. The method allows us to choose the cyclic operators and corresponding generating function selectively, depending on initial problem for analytical or numerical study. Our approach includes, as a particular case, the perturbation theory, but generally does not require inside any small parameters and unperturbed solutions. We demonstrate the applicability of the method to the analysis of several differential equations in mathematical physics, namely, classical oscillator, Schrodinger equation, and wave equation in dispersive medium.