We establish the existence of positive periodic solutions of the second-order singular coupled systems{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）） ...We establish the existence of positive periodic solutions of the second-order singular coupled systems{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）,where pi, qi, ci ∈ C（R/T Z; R）, i = 1, 2; f_1, f_2 ∈ C（R/T Z ×（0, ∞）, 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.展开更多
State feedback and pole assignment of the second order coupled singular distributed parameter systems are discussed via functional analysis and operator theory in Hilbert space, in which infinite many poles are change...State feedback and pole assignment of the second order coupled singular distributed parameter systems are discussed via functional analysis and operator theory in Hilbert space, in which infinite many poles are changed. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the pole assignment and stabilization of the singular distributed parameter systems.展开更多
基金Supported by the Scientific Research Funds for the Ningxia Universities(Grant No.NGY2015141)
文摘We establish the existence of positive periodic solutions of the second-order singular coupled systems{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）,where pi, qi, ci ∈ C（R/T Z; R）, i = 1, 2; f_1, f_2 ∈ C（R/T Z ×（0, ∞）, 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.
基金supported by the National Nature Science Foundation of China under Grant No.60674018
文摘State feedback and pole assignment of the second order coupled singular distributed parameter systems are discussed via functional analysis and operator theory in Hilbert space, in which infinite many poles are changed. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse of bounded linear operator. This research is theoretically important for studying the pole assignment and stabilization of the singular distributed parameter systems.
