We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with ...We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable （1＋1）-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of hi-directional SK equations with self-consistent展开更多
The main desire of this paper is to present several new interval oscillation criteria related to a generalized Riccati technique for certain second-order nonlinear differential equations.Our results extend some known ...The main desire of this paper is to present several new interval oscillation criteria related to a generalized Riccati technique for certain second-order nonlinear differential equations.Our results extend some known equations.Finally,several examples illustrate the effectiveness of our results.展开更多
For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied. The criterion equation of the Noe...For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied. The criterion equation of the Noether symmetry for the system is got. The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained. Finally, an example is given to illustrate the application of the results.展开更多
We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves r...We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves related contributions to the subject. An example is provided to illustrate assumptions in our theorem are less restrictive.展开更多
基金supported by National Basic Research Program of China (973 Program) under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10601028the Natural Science Foundation of Fujian Province under Grant No.2008J0199
文摘We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable （1＋1）-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of hi-directional SK equations with self-consistent
基金Supported by Science Foundation for Young Teachers of Northeast Normal University（20080105） Supported by NSFC（10926105+2 种基金1100104110971022） Supported by SRFDP（200802001008）
文摘The main desire of this paper is to present several new interval oscillation criteria related to a generalized Riccati technique for certain second-order nonlinear differential equations.Our results extend some known equations.Finally,several examples illustrate the effectiveness of our results.
文摘In this paper the author proves that the Phragmen Lindelof principle holds for solutions of elliptic equation (1) with nonstandard growth conditions.
文摘For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied. The criterion equation of the Noether symmetry for the system is got. The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained. Finally, an example is given to illustrate the application of the results.
基金supported by the Applied Mathematics Enhancement Program of Linyi University
文摘We establish a new Kamenev-type theorem for a class of second-order nonlinear damped delay dynamic equations on a time scale by using the generalized Riccati transformation technique. The criterion obtained improves related contributions to the subject. An example is provided to illustrate assumptions in our theorem are less restrictive.
