LECTURES ON TOPICS IN NONLINEAR DIFFERENTIAL EQUATIONS,

Abstract

These lectures describe some recent researches by the author and one of his graduate students at Oxford University on ordinary nonlinear differential equations. The first lecture is devoted to a search for a 'superposition' principle for these nonlinear equations and it determines the class of nonlinear equations for which such a superposition principle exists. The remaining four lectures provide a rigorous, analytical theory of the technique invented by Lighthill (1949) for solving nonlinear differential equations with an 'irregular' perturbation. Such equations involve a small parameter alpha and such that the coefficient of the highest derivative vanishes identically, or at the 'initial point', when alpha = 0. The theory is developed from a number of simple examples and given a rigorous form by means of the theory of 'dominant functions'. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1960
Accession Number
AD0631190

Entities

People

  • G. Temple

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Differential Equations
  • Equations
  • Linear Differential Equations
  • Mathematical Analysis
  • Mathematics
  • Nonlinear Differential Equations
  • Perturbations
  • Real Variables
  • Students

Fields of Study

  • Mathematics

Readers

  • Academic Conference Management
  • Calculus or Mathematical Analysis