Positive Periodic Solutions of Second-Order Singular Coupled Systems with Damping Terms
Received:December 08, 2016  Revised:May 17, 2017
Key Word: positive periodic solutions   singular coupled systems   Schauder's fixed point theorem   weak singularities
Fund ProjectL:Supported by the Scientific Research Funds for the Ningxia Universities (Grant No.NGY2015141).
 Author Name Affiliation Ruipeng CHEN Department of Mathematics, North Minzu University, Ningxia 750021, P. R. China Xiaoya LI Department of Mathematics, North Minzu University, Ningxia 750021, P. R. China
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Abstract:
We establish the existence of positive periodic solutions of the second-order singular coupled systems \left\{ \aligned x''+p_1(t)x'+q_1(t)x=f_1(t,y(t))+c_1(t),\\ y''+p_2(t)y'+q_2(t)y=f_2(t,x(t))+c_2(t),\\ \endaligned\right. where $p_i,\ q_i,\ c_i\in C(\mathbb{R}/T\mathbb{Z};\mathbb{R}),\ i=1,2$;\ \ $f_1,\ f_2\in C(\mathbb{R}/T\mathbb{Z}\times(0,\infty),\mathbb{R})$ and may be singular near the zero. The proof relies on Schauder's fixed point theorem and anti-maximum principle. Our main results generalize and improve those available in the literature.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.04.005