The Second-Order Self-Adjoint Equation With Mixed Derivatives

Abstract

In this chapter, we are concerned with the second-order, self-adjoint dynamic equation P(T)X(SUB TRIANGLE UP)(T)(sup triangle down) + q(t)x(t) = 0 on a time scale. Since this equation combines both A and V derivatives in the same equation, we will begin by examining how these two types of derivatives interact. We will then study some basic results concerning this equation, specifically the Lagrange Identity and Abel's Formula. The remainder of the chapter will cover zeros of solutions and disconjugacy, including factorizations and Riccati techniques. The material in this chapter has been previously published in 8 and 7.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 14, 2002
Accession Number
ADA406708

Entities

People

  • Kirsten R. Messer

Organizations

  • University of Nebraska–Lincoln

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Coefficients
  • Complex Numbers
  • Department Of Defense
  • Difference Equations
  • Differential Equations
  • Electronic Mail
  • Equations
  • Exponential Functions
  • Identities
  • Integrals
  • Intervals
  • Mathematics
  • Nebraska
  • Numbers
  • Riccati Equation
  • United States

Fields of Study

  • Mathematics

Readers

  • Business Analytics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra