Positive periodic solutions of Hill’s equations with singular nonlinear perturbations

✍ Scribed by Jifeng Chu; Ming Li

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 278 KB
• Volume: 69
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.05.016

✦ Synopsis

We study the existence and multiplicity of positive periodic solutions of Hill's equations with singular nonlinear perturbations. The new results are applicable to the case of a strong singularity as well as the case of a weak singularity. The proof relies on a nonlinear alternative principle of Leray-Schauder and a fixed point theorem in cones. Some recent results in the literature are generalized and improved.