Existence and Multiplicities of Solutions for Asymptotically Linear Ordinary Differential Equations Satisfying Sturm-Liouville BVPs with Resonance

摘要

In this paper, we prove existence and multiplicities of solutions for asymptotically linear ordinary differential equations satisfying Sturm-Liouville boundary value conditions with resonance. Adding assumption H _( 3 ) that is similar to (LL) in Theorem 1.1, by index theory and Morse theory, we obtain more nontrivial solutions.