Existence and multiplicity of weak solutions for a nonlinear impulsive ( q , p ) $(q,p)$ -Laplacian dynamical system

Abstract

Abstract In this paper, we investigate the existence and multiplicity of nontrivial weak solutions for a class of nonlinear impulsive ( q , p ) $(q,p)$ -Laplacian dynamical systems. The key contributions of this paper lie in (i) Exploiting the least action principle, we deduce that the system we are interested in has at least one weak solution if the potential function has sub- ( q , p ) $(q,p)$ growth or ( q , p ) $(q,p)$ growth; (ii) Employing a critical point theorem due to Ding (Nonlinear Anal. 25(11):1095-1113, 1995), we derive that the system involved has infinitely many weak solutions provided that the potential function is even.

Keywords

• ( q , p ) $(q,p)$ -Laplacian
• existence
• multiplicity
• nontrivial solution
• variational methods