Variational approach for a p-Laplacian boundary value problem on time scales

ABSTRACT

In this paper, we study a second-order p-Laplacian dynamic equation on a periodic time scale subject to certain boundary value conditions. The variational structure of the above-mentioned boundary value problem is presented. Some new results on the existence of at least one or three distinct periodic solutions are established by means of the saddle point theorem, the least action principle as well as the three critical point theorem.

KEYWORDS:

• Time scales
• variational structure
• p-Laplacian
• boundary value problem
• periodic solution
• critical point theorem

AMS SUBJECT CLASSIFICATIONS:

• 35M12
• 34B15
• 65L10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NSF [DMS-1204497] and NSF of China [grant number 11361047].