ON A BOUNDARY-VALUE PROBLEM,

Abstract

The differential equation considered in the paper is Phi' = f(x, Phi) psi (x) with conditions Phi (0) = y sub o, R Phi' (R) - Phi (R) = q for 0 < or x < = R, where yo,R,q are given real numbers, y sub o > O, R > O. The solution sought, phi(x), is to be non-negative. A number of conditions are imposed on f(x,phi) and psi. Problems of this type are encountered in the statistical theory of the atom, and these conditions follow naturally from the physical setting of the problems. Continuous dependence of the interval of existence of the solution and the continuous dependence of the solution itself on the boundary values are established. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 08, 1966
Accession Number
AD0648352

Entities

People

  • R. I. Anishchenko

Organizations

  • Johns Hopkins University Applied Physics Laboratory

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Equations
  • Intervals
  • Numbers
  • Real Numbers

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.