Variational approach to non-instantaneous impulsive differential equations with $ p $-Laplacian operator

Abstract

<abstract><p>In this paper, we consider the existence, multiplicity and nonexistence of solutions for a class of $ p $-Laplacian differential equations with non-instantaneous impulses. By using variational methods and critical point theory, we obtain that the impulsive problem has at least one nontrivial solution, at least two nontrivial solutions and no nontrivial solution.</p></abstract>