Three nonnegative solutions for Sturm-Liouville BVP and application to the complete Sturm-Liouville equations

Abstract

The main purpose of this manuscript is to investigate the Sturm-Liouville BVP for non-autonomous Lagrangian systems. Under the suitable assumptions, we establish an existence theorem for three nonnegative solutions via Bonanno-Candito's three critical point theory. As an application in the complete Sturm-Liouville equations with Sturm-Liouville BVC, we get an existence theorem of three nonnegative solutions. Meanwhile, we give three examples to show the correctness of our results.

Keywords

• sturm-liouville bvc
• lagrangian systems
• critical points
• index theory
• complete sturm-liouville equations