Ekeland变分原理的推广及其应用

本文首先将Ekeland变分原理推广成一般的形式,然后考虑(P.S.)′条件与泛函的强制性之间的关系.     

ON THE EXISTENCE OF GLOBAL ATTRACTOR FOR A CLASS OF INFINITE DIMENSIONAL DISSIPATIVE NONLINEAR DYNAMICAL SYSTEMS

By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.     

Existence of global attractors for the coupled system of suspension bridge equations

A mathematical model of the suspension bridge describes the vibration of the road bed in the vertical plain and that of the main cable. We show the existence of an absorbing set for the solution of the problem. Furthermore, the global attractors of the coupled system of suspension bridge are studied by a new semigroup approach.     

S^1*S^1-INDEX THEORY ON PRODUCT SPACE

A new index is constructed by use of the canonical representation of S1 x S1 group over a product space. This index satisfies the general properties of the usual index but does not satifsy the dimension property. As an application, two abstract critical point theorems are given.     

{\tf S}$^{\bold 1}${\td X}{\tf S}$^{\bold 1}$-INDEX THEORY ON PRODUCT SPACE

A new index is constructed by use of the canonical representation of $S^1\times S^1$ group over a product space. This index satisfies the general properties of the usual index but does not satifsy the dimension property. As an application, two abstract critical point theorems are given.