The existence of periodic solutions for nonlinear systems of first-order differential equations at resonance |
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Authors: | MA Shi-wang Associate Professor Doctor Wang Zhi-cheng Yu Jian-she |
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Affiliation: | (1) Department of Applied Mathematics, Shanghai Jiaotong University, 200030 Shanghai, P R China;(2) Department of Applied Mathematics, Human University, 410082 Changsha, P R China |
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Abstract: | The nonlinear system of first-order differential equations with a deviating argument is considered, where x(t)εR 2, τεR, BεR 2×2, F is bounded and p(t) is continuous and 2π-periodic. Some sufficient conditions for the existence of 2π-periodic solutions of the above equation, in a resonance case, by using the Brouwer degree theory and a continuation theorem based on Mawhin's coincidence degree are obtained. Some applications of the main results to Duffing's equations are also given. Foundation item: the National Natural Science Foundation of China (19801014, 19971026, 19831030) Biography: MA Shi-wang (1965-) |
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Keywords: | first-order differential equation periodic solution resonance Brouwer degree coincidence degree Duffing equation |
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