Lower and Upper Solution Method for Semilinear, Quasi-Linear and Quadratic Singularly Perturbed Neumann Boundary Value Problems

Abstract

In this paper, by using the method of lower and upper solutions and notion of (Iq)-stability, we established sufficient conditions for the uniform convergence of the solutions of singularly perturbed Neumann boundary value problems for second-order differential equations to the solution of their reduced problems.

Keywords

• second-order ordinary differential equation
• singular perturbation
• Neumann boundary condition
• semilinear problem
• quasi-linear problem
• quadratic problem