Existence of multiple positive periodic solutions for delay differential equation whose order is a multiple of 4 |
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| Authors: | Julio G Dix Seshadev Padhi |
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| Institution: | 1. Department of Mathematics, Texas State University, 601 University Dr., San Marcos, TX 78666, USA;2. Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi 835 215, India;1. School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, PR China;2. College of Mathematics, Southwest Jiaotong University, Chengdu 610031, PR China;1. Department of Mathematics, Lingnan Normal University, Zhanjiang, Guangdong 524048, PR China;2. Department of Mathematics, Hechi University, Yizhou, Guangxi 546300, PR China;3. School of Mathematics and Computer, Guangdong Ocean University, Zhanjiang, Guangdong 524088, PR China |
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| Abstract: | This article shows the existence of positive periodic solutions for retarded, advanced, neutral, and ordinary differential equations whose order is a multiple of 4. First, we find a positive Green’s function explicitly. Then assuming that the coefficient of the unknown in the linear part of the equation is bounded above and below by positive constants, we find one and then three solutions by applying the Krasnoselskii and Legget–William fixed point theorems. |
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