TITLE:
Existence and Multiplicities of Solutions for Asymptotically Linear Ordinary Differential Equations Satisfying Sturm-Liouville BVPs with Resonance
AUTHORS:
Keqiang Li, Ronghua Tong
KEYWORDS:
Asymptotically Linear Ordinary Differential Equations with Resonance, Multiple Solutions, Sturm-Liouville Boundary Value Problem, Index Theory, Morse Theory
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.5,
May
29,
2019
ABSTRACT: 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.