Accession Number : AD0278583

Title :   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

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : GROSS,O.A.

Report Date : AUG 1962

Pagination or Media Count : 1

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)

Descriptors :   ALGEBRA, IONIZATION POTENTIALS, PARTICLES

Distribution Statement : APPROVED FOR PUBLIC RELEASE