On Leighton's comparison theorem

Academic Article


  • © 2017 Elsevier Inc. We give a simple proof of a fairly flexible comparison theorem for equations of the type −(p(u′+su))′+rp(u′+su)+qu=0 on a finite interval where 1/p, r, s, and q are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand. We illustrate this by presenting some examples and special cases which include Schrödinger equations with distributional potentials as well as Jacobi difference equations.
  • Authors

    Published In

    Digital Object Identifier (doi)

    Author List

  • Ghatasheh A; Weikard R
  • Start Page

  • 5978
  • End Page

  • 5989
  • Volume

  • 262
  • Issue

  • 12