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.

General Exact Schemes for Second-Order Linear Differential Equations Using the Concept of Local Green Functions

“…The fundamental recursive formula is obtained by adding Equation (16) and Equation (18), and using the equalities…”

“…One of these directions is the study of symbolic approaches related to non-linear ODEs and systems, the so-called reaction-diffusion, cross-diffusion equations [13,14]. Further, the research group is ambitious in studying other types of non-linear ODEs, which are still intensively researched today [15][16][17]. The second research area is the inverse problems involving second-order differential equations, which are also non-linear mathematical problems [18].…”