Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 2, pp. 38 – 44
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0130
Multiplicity results for a class of nonlinear singular differential equation with a parameter
Shaowen Li\(^{1,*}\)
\(^{1}\) School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China.
Copyright © 2023 Shaowen Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: June 27, 2023 – Accepted: July 15, 2023 – Published: December 29, 2023
Abstract
This paper gives sufficient conditions for the existence of positive periodic solutions to general indefinite singular differential equations. Furthermore, under some assumptions we show the existence of two positive periodic solutions. The methods used are Krasnoselski\(\breve{\mbox{i}}\)’s-Guo fixed point theorem and the positivity of the associated Green’s function.
Keywords:
Indefinite singularity; Positive periodic solution; Krasnoselski$\breve{\mbox{i}}$’s-Guo fixed point; Green’s function