Periodic solutions of second order non-autonomous singular dynamical systems |
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Authors: | Jifeng Chu Pedro J Torres Meirong Zhang |
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Institution: | a Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China b College of Science, Hohai University, Nanjing 210098, China c Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain |
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Abstract: | In this paper, we establish two different existence results of positive periodic solutions for second order non-autonomous singular dynamical systems. The first one is based on a nonlinear alternative principle of Leray-Schauder and the result is applicable to the case of a strong singularity as well as the case of a weak singularity. The second one is based on Schauder's fixed point theorem and the result sheds some new light on problems with weak singularities and proves that in some situations weak singularities may help create periodic solutions. Recent results in the literature are generalized and significantly improved. |
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Keywords: | 34B15 34B16 34D20 |
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