Bifurcation curves for singular and nonsingular problems with nonlinear boundary conditions

Abstract

We discuss a quadrature method for generating bifurcation curves of positive solutions to some autonomous boundary value problems with nonlinear boundary conditions. We consider various nonlinearities, including positone and semipositone problems in both singular and nonsingular cases. After analyzing the method in these cases, we provide an algorithm for the numerical generation of bifurcation curves and show its application to selected problems.

Keywords

• Quadrature method
• bifurcation curve
• existence
• singular problems
• nonlinear boundary condition