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A Class of Definite Boundary Problems

  • William T. Reid
Part of the Applied Mathematical Sciences book series (AMS, volume 31)

Abstract

Antedating the work of Morse on the extension of the Sturmian theory to self-adjoint differential systems, Bliss [2] considered a real two-point boundary problem which in terms of an n-dimensional vector function y(t) = (yα(t)), (α = l,…, n), may be written as
$$ (a)y'(t) = A(t)y(t) + \lambda B(t)y(t),\quad t \in \left[ {a,b} \right].(b)s\left[ y \right] \equiv My(a) + Ny(b) = 0. $$
(1.1)
For such a system he introduced the concept of “self-adjointness under a real non-singular transformation z = T(t)y”, and considered in detail a special class of such problems which he called “definitely self-adjoint”. This class of problems included the so-called accessory boundary problem for a non-singular simple integral variational problem involving no auxiliary differential equations as restraints, but included the accessory problem for a variational problem of Lagrange or Bolza type only in case the condition of identical normality held.

Keywords

Vector Function Boundary Problem Differential System Boundary Prob Normality Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • William T. Reid
    • 1
  1. 1.Department of MathematicsUniversity of OklahomaUSA

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