On the index of the global attractor for a class of -Laplacian equations

Existence of multiple equilibrium points in global attractor for damped wave equation

“…From [5] we know that any compact set A with fractal dimension dim F A = n can be mapped into R 2n+1 by a linear odd Hölder-continuous one-to-one projector. Similar to Corollary 1.1 in [17], we have the following corollary.…”

On the Z<inf>2</inf> index of global attractor for odd dynamical systems and application

“…In this paper, we extend the results in [1] for p-Laplacian equation to general odd dynamical systems by use of 2 index. It is know that the 2 index of a symmetric set reflects the topology of (see [16]), and from the Mane projection theorem (see [17]),we know that if the 2 index of a set is larger than 2 + 1, then the fractal dimension of is larger than .…”

“…However, the geometry of global attractor can be very complicated, in [15], the authors considered the finite and infinite dimensional global attractor for porous media equation. And recently, in [1], applying 2 index, the authors provided a new approach to study the geometry of global attractor for p-Laplacian equation, and constructed a finite dimensional global attractor and a infinite dimensional global attractor for p-Laplacian equations.…”

Category of Attractor and Its Application

“…To study the geometry of the attractors, some concepts such as Lyapunov exponents, the Hausdorff dimension and the fractal dimension were also proposed, see [3] [4] etc. Recently, in [5] author studied the geometrical property of the global attractor for a class of symmetric p-Laplacian equations by means of 2 Z index, obtained some lower estimates for the fractal dimension of the global attractor. In this paper, by using Ljusternik-Schnirelmann category (category for short), we try to provide a new approach to studying the geometry of the global attractor.…”