Stability inequalities for one-dimensional singular perturbation problems

Abstract

AbstractWe establish stability inequalities for quasi-linear singularly perturbed twopoint boundary value problems. Our approach uses integral representations of the exact solution in terms of different approximate solutions, like the WKB asymptotic solutions. We prove our inequalities under conditions which are more general than those required for the similar results obtained by Lorenz in 1982 and by Kopteva in 2001. This is illustrated by several examples. Moreover, an example of the nonturning-point case shows that our inequalities are sharper.