Abstract
Using Leray–Schauder degree theory, we investigate the existence and multiplicity of positive T-periodic solutions to Minkowski-curvature equations with a singularity of attractive type
where \(f\in C((0,+\infty ),\mathbb {R})\), \(\varphi \in C(\mathbb {R},\mathbb {R})\) and \(r\in C(\mathbb {R},(0,+\infty ))\) are T-periodic functions, m and \(\mu \) are two positive constants and \(0<m\le 1\), \(s\in \mathbb {{R}}\) is a parameter. Based on a new method to construct upper and lower functions and some properties of Leray–Schauder degree, a multiplicity result of Ambrosetti-Prodi type is established.
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Research is supported by Technological Innovation Talents in Universities and Colleges in Henan Province (21HASTIT025), Natural Science Foundation of Henan Province (222300420449) and Innovative Research Team of Henan Polytechnic University (T2022-7).
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Cheng, Z., Kong, C. & Xia, C. Multiple Positive Periodic Solutions to Minkowski-Curvature Equations with a Singularity of Attractive Type. Qual. Theory Dyn. Syst. 21, 146 (2022). https://doi.org/10.1007/s12346-022-00680-0
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DOI: https://doi.org/10.1007/s12346-022-00680-0
Keywords
- Minkowski-curvature operator
- Singularity of attractive type
- Positive periodic solutions
- Leray–Schauder degree theory
- Upper and lower functions