Investigation of Characteristic Curve for Sturm–Liouville Problem with Nonlocal Boundary Conditions on Torus

Abstract

In this paper, we investigate the second-order Sturm–Liouville problem with two additional Nonlocal Boundary Conditions. Nonlocal boundary conditions depends on two parameters. We find condition for existence of zero eigenvalue in the parameters space and classified Characteristic Curves in the plane and extended plane is described as torus. The Characteristic Curve on torus may be of three types only. Some new conclusions about existence and uniqueness domain of solution are presented.

Keywords:

• Sturm–Liouville problem
• Nonlocal Boundary Conditions
• Torus

AMS Subject Classification:

• 34B24
• 34B10