Sturm-Liouville Problems with Several Parameters.

Abstract

We consider the regular linear Sturm-Liouville problem (second-order linear ordinary differential equation with boundary conditions at two points x= 0 and x = 1, those conditions being separated and homogeneous) with several real parameters lambda 1, lambda N. Solutions to those problems correspond to eigenvalues lambda = (lambda 1, lambda N) lying on surfaces in R superscript N determined by the number of zeroes in (0,1) of solutions. We describe properties of these surfaces, including: boundedness, and when unbounded, asymptotic directions. Using these properties some results are given for the system of N Sturm-Liouville problems which share only the parameters. Sharp results are given for the system of two problems sharing two parameters.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1979
Accession Number
ADA072617

Entities

People

  • Lawrence Turyn

Organizations

  • Brown University

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Analytic Functions
  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Eigenvalues
  • Equations
  • Inequalities
  • Linear Algebra
  • Mathematics
  • New York
  • Oscillation
  • Rhode Island
  • Rotation
  • Sequences
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Control Systems Engineering.
  • Fluid Dynamics.