Multiple equilibrium points in global attractors for some p-Laplacian equations

Abstract

In this paper, we continue to study the properties of the global attractor for some p-Laplacian equations with a Lyapunov function F in a Banach space when the origin is no longer a local minimum point but a saddle point of F. By using the abstract result established in our previous work, we prove the existence of multiple equilibrium points in the global attractor for some p-Laplacian equations under some suitable assumptions in the case that the origin is an unstable equilibrium point.

Keywords:

• Lyapunov function
• global attractor
• -index
• equilibrium point
• p-Laplacian

AMS Subject Classifications:

• 35Q35
• 35B40
• 37C60

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Science Foundation of China [grant number 11401459], [grant number 11031003].