On the solutions of a second order nonlinear system with almost periodic forcing |
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| Institution: | 1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China;2. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China;1. School of Mathematics, Sichuan University, Chengdu 610064, Sichuan, PR China;2. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, PR China;3. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, PR China;4. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, PR China;5. Department of Mathematical & Statistical Sci, University of Alberta, Edmonton Alberta, Canada T6G 2G1;6. School of Mathematics, Jilin University, Changchun 130012, PR China;7. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA;1. Dipartimento di Matematica e Geoscienze, Università di Trieste, P.le Europa 1, I-34127 Trieste, Italy;2. Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche 12, 60131 Ancona, Italy |
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| Abstract: | A second order almost periodic perturbed nonlinear system with small parameter is discussed in this paper. Based on some analytical techniques and the method of averaging, some sufficient conditions are obtained for existence of one almost periodic solution. Also some suitable conditions are given for existence of two almost periodic solutions. The obtained new results generalized the known results in Seifert 1], 3] and He 2], 4]. Finally, some applications are presented to illustrate that our results are a good generalization of the known results. |
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