By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_...By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_{n - 1} + f(n, x_n ) = 0,$$ some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.展开更多
For the real planar autonomous differential system, the questionsof detection between center and focus, successor function, formal series, central integration, integration factor, focal values, values of singular poin...For the real planar autonomous differential system, the questionsof detection between center and focus, successor function, formal series, central integration, integration factor, focal values, values of singular point and bifurcation of limit cycles for a class of higher-degree critical points and infinite points are expounded.展开更多
基金This work was supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE of Chinaby the Trans-Century Training Programme Foundation for the Talents of the State Education Commissionby the National Natural Science Foundation of China(Grant No.19831030).
文摘By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_{n - 1} + f(n, x_n ) = 0,$$ some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.
基金This work was supported by the Natural Science Foundation of Hunan Province (Grant No. 10071016) .
文摘For the real planar autonomous differential system, the questionsof detection between center and focus, successor function, formal series, central integration, integration factor, focal values, values of singular point and bifurcation of limit cycles for a class of higher-degree critical points and infinite points are expounded.
