Advertisement

The Existence and Continuous Dependence Theorem for Solutions of Differential Equations

  • R. V. Gamkrelidze
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 7)

Abstract

The basic result of this chapter is formulated in Theorems 4.3 and 4.4 on the existence and continuous dependence of solutions of differential equations on the initial data and right-hand sides. These theorems are formulated and proved in Sections 4.4 and 4.5, and they appear as comparatively easy corollaries of Theorem 4.2 on the existence and continuous dependence of solutions of differential equations with fixed right-hand sides, which is proved in Section 4.3. The technique used for deriving Theorems 4.3 and 4.4 from Theorem 4.2 is standard, and it often turns out to be very useful.

Keywords

Compact Support Contraction Mapping Continuous Dependence Unique Fixed Point Contraction Coefficient 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • R. V. Gamkrelidze
    • 1
  1. 1.Steklov InstituteMoscowU.S.S.R.

Personalised recommendations