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.