Singular Quadratic Functionals,

Abstract

The study of quadratic forms is an important part of variational theory. When a quadratic form that is an integral is nonsingular in the sense that a strengthened Legendre condition holds, then we can use an index theory of quadratic forms to obtain information about minimization problems, comparison and oscillation theorems for differential equations, the theory of conjugate and focal points, boundary value problems for differential equations and the Sturm Liouville theory for self-adjoint systems of differential equations, and the theory of eigenvalues. The index theory mentioned above is sometimes referred to as a local Morse theory. The purpose of this study is to see what can be said for each of these problems when the quadratic form is singular at only the endpoints. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1971
Accession Number
AD0725589

Entities

People

  • Junior Stein

Organizations

  • University of California, Los Angeles

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Eigenvalues
  • Equations
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Oscillation

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra