ON A CLASS OF DIFFERENTIAL EQUATIONS FOR VECTOR-VALUED DISTRIBUTIONS,

Abstract

The aim of this paper is to seek necessary and sufficient conditions on the linear operator A in a linear topological space in order that the Cauchy problem for the equation (U superscript alpha)-(the product of A and U) = T should be well set in the sense of distributions. Here O < alpha < infinity, U superscript alpha is the fractional derivative of U of order alpha. Such conditions are obtained for alpha integer = or > and then for any alpha > O, this time with the additional assumption of (at most) exponential growth of the solutions at infinity. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1968
Accession Number
AD0687069

Entities

People

  • H. O. Fattorini

Organizations

  • University of California, Los Angeles

Tags

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Cauchy Problem
  • Differential Equations
  • Equations
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Calculus or Mathematical Analysis
  • Statistical inference.

Technology Areas

  • Space