Conjugate points of vector-matrix differential equations

Academic Article

Abstract

  • The system of equations (Formula Presented) is considered where the coefficients are real, continuous, symmetric matrices, y is a vector, and P0(x) is positive definite. It is shown that the well-known quadratic functional criterion for existence of conjugate points for this system can be further utilized to extend results of the associated scalar equation to the vector-matrix case, and in some cases the scalar results are also improved. The existence and nonexistence criteria for conjugate points of this system are stated in terms of integral conditions on the eigenvalues or norms of the coefficient matrices. © 1977 American Mathematical Society.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Lewis RT
  • Start Page

  • 167
  • End Page

  • 178
  • Volume

  • 231
  • Issue

  • 1