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