(Iq)-Stability and Uniform Convergence of the Solutions of Singularly Perturbed Boundary Value Problems

In this paper, using the notion of (I-q)-stability and the method of a priori estimates, known as the method of lower and upper solutions, the sufficient conditions guaranteeing uniform convergence of solutions to the solution of a reduced problem on the entire interval [a, b] have been established for four different types of boundary conditions for a singularly perturbed differential equation epsilon y '' = f (x, y, y '), a <= x <= b. In the second part of the paper, by employing the Peano phenomenon, we analyzed the structure of the solutions of the reduced problem f (x, y, y') = 0.