Electron. J. Differential Equations, Vol. 2018 (2018), No. 26, pp. 1-12.

Bifurcation curves for singular and nonsingular problems with nonlinear boundary conditions

Jerome Goddard II, Quinn Morris, Ratnasingham Shivaji, Byungjae Son

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.

Submitted June 7, 2017. Published January 18, 2018.
Math Subject Classifications: 34B18.
Key Words: Quadrature method; bifurcation curve; existence; singular problems; nonlinear boundary condition.

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Jerome Goddard, II
Department of Mathematics & Computer Science
Auburn University at Montgomery
Montgomery, AL 36117, USA
email: jgoddard@aum.edu
Quinn Morris
Department of Mathematics & Statistics
Swarthmore College
Swarthmore, PA 19342, USA
email: qmorris1@swarthmore.edu
Ratnasingham Shivaji
Department of Mathematics & Statistics
University of North Carolina at Greensboro
Greensboro, NC 27412, USA
email: r_shivaj@uncg.edu
Byungjae Son
Department of Mathematics
Wayne State University
Detroit, MI 48202, USA
email: gm5431@wayne.edu

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