In this paper,we show the asymptotic stability in the large of the trivial solution x 0 for case p=0 and the boundedness result of solutions(1.1) for case p≠0.The resultobtained here extend the author's results i...In this paper,we show the asymptotic stability in the large of the trivial solution x 0 for case p=0 and the boundedness result of solutions(1.1) for case p≠0.The resultobtained here extend the author's results in[3].AMS Classification numbers:34D20,34D99展开更多
A numerical method is developed to evaluate the dynamic stability parameters of aircraft. This method is based on the aerodynamic model proposed by Etkin. His model is analyzed and generalized. After giving the specif...A numerical method is developed to evaluate the dynamic stability parameters of aircraft. This method is based on the aerodynamic model proposed by Etkin. His model is analyzed and generalized. After giving the specific forms of the aerodynamic model, the dynamic stability parameters are determined by the unsteady flow field computation and a parameter identification technique. Numerical experiments show that this method is accurate in predicting the dynamic stability characteristics of blunt cones in hypersonic flight.展开更多
In this paper,the existence of stationary oscillations of second order periodic systemsunder stochastlc noise interference is investigated,and the necessary and sufficient condition for the existence of stationary osc...In this paper,the existence of stationary oscillations of second order periodic systemsunder stochastlc noise interference is investigated,and the necessary and sufficient condition for the existence of stationary oscillations in the sense of mean-square stability is obtained via establishing equivalent vector stochastic systems and establishing deterministicequivalent systems in the sense of stability, and applying the existence theorem of stationary oscillations for the deterministic systems.展开更多
Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It ...Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ*> 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r^(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] .展开更多
文摘In this paper,we show the asymptotic stability in the large of the trivial solution x 0 for case p=0 and the boundedness result of solutions(1.1) for case p≠0.The resultobtained here extend the author's results in[3].AMS Classification numbers:34D20,34D99
文摘A numerical method is developed to evaluate the dynamic stability parameters of aircraft. This method is based on the aerodynamic model proposed by Etkin. His model is analyzed and generalized. After giving the specific forms of the aerodynamic model, the dynamic stability parameters are determined by the unsteady flow field computation and a parameter identification technique. Numerical experiments show that this method is accurate in predicting the dynamic stability characteristics of blunt cones in hypersonic flight.
文摘In this paper,the existence of stationary oscillations of second order periodic systemsunder stochastlc noise interference is investigated,and the necessary and sufficient condition for the existence of stationary oscillations in the sense of mean-square stability is obtained via establishing equivalent vector stochastic systems and establishing deterministicequivalent systems in the sense of stability, and applying the existence theorem of stationary oscillations for the deterministic systems.
基金supported by the National Natural Science Foundation of China(Nos.11201119,11471099)the International Cultivation of Henan Advanced Talents and the Research Foundation of Henan University(No.yqpy20140043)
文摘Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ*> 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r^(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] .
