Author(s)

Keqiang Li, Ronghua Tong

Department of Mathematics, Henan Normal University, Xinxiang, China.

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 H₃ that is similar to (LL) in Theorem 1.1, by index theory and Morse theory, we obtain more nontrivial solutions.

Asymptotically Linear Ordinary Differential Equations with Resonance, Multiple Solutions, Sturm-Liouville Boundary Value Problem, Index Theory, Morse Theory

Li, K. and Tong, R. (2019) Existence and Multiplicities of Solutions for Asymptotically Linear Ordinary Differential Equations Satisfying Sturm-Liouville BVPs with Resonance. Journal of Applied Mathematics and Physics, 7, 1197-1211. doi: 10.4236/jamp.2019.75080.