Positive periodic solutions of Hill’s equations with singular nonlinear perturbations |
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Authors: | Jifeng Chu Ming Li |
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Affiliation: | 1. Department of Applied Mathematics, College of Science, Hohai University, Nanjing 210098, PR China;2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China |
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Abstract: | 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. |
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Keywords: | 34B15 34B16 34D20 |
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