Coincidence Theory of a Nonlinear Periodic Sturm–Liouville System and Its Applications

Abstract

Based on the second derivative, this paper directly establishes the coincidence degree theory of a nonlinear periodic Sturm–Liouville (SL) system. As applications, we study the existence of periodic solutions to the S–L system with some special nonlinear functions by applying Mawhin’s continuation theorem. Some examples and simulations are furnished to inspect the correctness and availability of the chief findings.

Keywords

• nonlinear S–L system
• periodic solution
• existence
• coincidence degree theory