By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differenti...By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differential equation in Banach spaces is obtained and the related results are essentially improved.At the same time, another sufficient condition of existence of minimal and maximal solutions based on the Kuratowski measure of noncompactness is given.展开更多
The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are establi...The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are established.展开更多
A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. Th...A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained.展开更多
This paper is concerned with the effects of redundant control inputs on the quadratic optimal performance index in finite-time optimal control.Actually,the effects of redundant control input on quadratic performance i...This paper is concerned with the effects of redundant control inputs on the quadratic optimal performance index in finite-time optimal control.Actually,the effects of redundant control input on quadratic performance index is equal to study the effects of the redundant control input on the solution of Riccati differential equation(RDE).Hence,some sufficient conditions are presented to strictly decrease the solution of RDE with the column of input matrix increased.Especially,a necessary and sufficient condition is derived to strictly decrease the solution of the homogeneous RDE after control input extensions.Moreover,one sufficient condition is obtained,which guarantees that the minimum control energy index strictly decreases with input extension.It is shown that redundant control inputs can improve the system performance based on these results.Some examples are taken to illustrate the effectiveness of related problems.展开更多
Abstract. In this paper the cubic homogeneous parameterized vector fields aJre studied.The classification of the phase portrait near the critical point is presented. This classifica- tion is an extension of the result...Abstract. In this paper the cubic homogeneous parameterized vector fields aJre studied.The classification of the phase portrait near the critical point is presented. This classifica- tion is an extension of the result given by Takens to the cubic homogeneous parameterizedvector fields with six parameters.展开更多
文摘By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differential equation in Banach spaces is obtained and the related results are essentially improved.At the same time, another sufficient condition of existence of minimal and maximal solutions based on the Kuratowski measure of noncompactness is given.
文摘The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are established.
基金This work is supported by the National Natural Science Foundation of China (Tian Yuan Foundation) (10426010) Natural Science Foundation of Fujian Province (Z0511052)Fujian Educational Bureau (JA04274).
文摘A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained.
基金supported by the National Natural Science Foundation of China under Grant Nos.61174038 and 61203129
文摘This paper is concerned with the effects of redundant control inputs on the quadratic optimal performance index in finite-time optimal control.Actually,the effects of redundant control input on quadratic performance index is equal to study the effects of the redundant control input on the solution of Riccati differential equation(RDE).Hence,some sufficient conditions are presented to strictly decrease the solution of RDE with the column of input matrix increased.Especially,a necessary and sufficient condition is derived to strictly decrease the solution of the homogeneous RDE after control input extensions.Moreover,one sufficient condition is obtained,which guarantees that the minimum control energy index strictly decreases with input extension.It is shown that redundant control inputs can improve the system performance based on these results.Some examples are taken to illustrate the effectiveness of related problems.
基金National Key Basic Research Special Fund(No.1998020307) National Natural Science Foundation of China(No.19990510).
文摘Abstract. In this paper the cubic homogeneous parameterized vector fields aJre studied.The classification of the phase portrait near the critical point is presented. This classifica- tion is an extension of the result given by Takens to the cubic homogeneous parameterizedvector fields with six parameters.
