THE BOUNDARY VALUE PROBLEM ON AN INFINITE INTERVAL. EXISTENCE, UNIQUENESS AND ASYMPTOTIC BEHAVIOR OF BOUNDED SOLUTIONS TO A CLASS OF NONLINEAR SECOND ORDER DIFFERENTIAL EQUATIONS

Abstract

A class of second-order nonlinear differential equations is studied. It is shown that, for a given member of the class and a given initial value, there exists a unique continuous bounded function on the nonnegative reals which satisfies the equation and the boundary value, and moreover that this function tends to a nonpositive constant as the argument tends to infinity. An applica ion is given to the asymptotic behavior of the bounded solution to the equation governing the motion of a particle in an ionized field under the influence of the Ukawa potential. Since topological methods seem inapplicable in the determination of isolated elements of noncompact spaces, a lattice theory is used. The key tool is a fixed-point theorem. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1962
Accession Number
AD0278583

Entities

People

  • O.a. Gross

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Equations
  • Intervals
  • Linear Differential Equations
  • Mathematical Analysis
  • Mathematics
  • Nonlinear Differential Equations
  • Point Theorem

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space