Multiplicity of positive periodic solutions to superlinear repulsive singular equations |
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Authors: | Daqing Jiang Jifeng Chu |
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Affiliation: | a Department of Mathematics, Northeast Normal University, Changchun 130024, Jilin, China b Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
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Abstract: | In this paper, we study positive periodic solutions to the repulsive singular perturbations of the Hill equations. It is proved that such a perturbation problem has at least two positive periodic solutions when the anti-maximum principle holds for the Hill operator and the perturbation is superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones. |
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Keywords: | Multiplicity Superlinear Repulsive singular equation Periodic solution |
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