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- 2015
二阶奇异耦合系统正周期解的存在性
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Abstract:
摘要： 运用Schauder不动点定理研究了二阶非自治奇异耦合系统 正周期解的存在性,其中ai, ei∈L1(R/TZ, R), fi∈Car(R/TZ×(0,∞), R),即fi|[0,T]:[0,T]×(0,∞)→R是L1-Carathéodory函数(i=1, 2),并且f1, f2分别在y=0, x=0处允许有奇性。在扰动项积分值符号同正、同负和异号的情况下,分别获得了该奇异耦合系统存在正周期解的条件。
Abstract: Using Schauder's fixed point theorem, we study the existence of positive periodic solutions for second order non-autonomous singular coupled systems where ai, ei∈L1(R/TZ, R), fi∈Car(R/TZ×(0,∞), R), that is, fi|[0,T]:[0,T]×(0,∞)→R are L1-Carathéodory functions(i=1, 2), and f1, f2 may be singular at y=0, x=0, respectively. The existence of positive periodic solutions for the singular coupled systems are obtained under the conditions that the signs of integral disturbance terms are positive, or negative, or different
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