Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 3, Pages 283-289
doi:10.1155/S1048953392000236
Multipoint focal boundary value problems on infinite intervals
University of Hyderabad, School of Mathematics and Computer Information Sciences, Central University P.O., Hyderabad 500 134, India
Received 1 October 1991; Revised 1 December 1991
Copyright © 1992 S. Umamaheswaram and M. Venkata Rama. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
For the differential equation y(n)=f(x,y), we state a set of
necessary and sufficient conditions for the existence of a solution (i) on a
semi-infinite interval for a k-point right focal boundary value problem
and (ii) on (−∞,∞) for a (n−1)-point right focal boundary value
problem. The conditions are in terms of the existence of a pair of
solutions u(x), v(x) satisfying some auxiliary boundary conditions and
algebraic inequatilities.