We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p 〉 2, -△p^u -= f（u） in R^2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The ex...We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p 〉 2, -△p^u -= f（u） in R^2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The existence of saddle solutions of the above problem was known only in dimensions 2m≥ 2p.展开更多
This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-eva...This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-evasion game since satellites in both sides will try their best to capture or escape. In this game, the distance of these two players is small enough so that the highly nonlinear earth-centered gravitational dynamics can be reduced to the linear Clohessy-Wiltshire（CW） equations. The system is then simplified by introducing the zero effort miss variables. Saddle solution is formulated for the pursuit-evasion game and time-to-go is estimated similarly as that for the exoatmospheric interception. Then a vector guidance is derived to ensure that the interception can be achieved in the optimal time. The proposed guidance law is validated by numerical simulations.展开更多
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11101134, 11371128） and the Young Teachers Program of Hunan University. The authors thank the anonymous referees for their valuable comments and suggestions.
文摘We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p 〉 2, -△p^u -= f（u） in R^2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The existence of saddle solutions of the above problem was known only in dimensions 2m≥ 2p.
基金co-supported by the National Natural Science Foundation of China (Nos.61603115,91438202 and91638301)China Postdoctoral Science Foundation (No.2015M81455)+1 种基金the Open Fund of National Defense Key Discipline Laboratory of Micro-Spacecraft Technology of China (No.HIT.KLOF.MST.201601)the Heilongjiang Postdoctoral Fund of China (No.LBH-Z15085)
文摘This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-evasion game since satellites in both sides will try their best to capture or escape. In this game, the distance of these two players is small enough so that the highly nonlinear earth-centered gravitational dynamics can be reduced to the linear Clohessy-Wiltshire（CW） equations. The system is then simplified by introducing the zero effort miss variables. Saddle solution is formulated for the pursuit-evasion game and time-to-go is estimated similarly as that for the exoatmospheric interception. Then a vector guidance is derived to ensure that the interception can be achieved in the optimal time. The proposed guidance law is validated by numerical simulations.
