Applications of variational method to impulsive $\bm{p}$-Laplacian problem with superlinear impulses

Abstract

{1.4}\\noindent{{\\bf Abstract} We consider the $p$-order superlinear impulsive differential equation\\begin{align*}\\label{1}\\begin{cases}-(|z(t)|^{p-2}z(t))=g(t,z(t),z(t)),and t\\neq t_{i}, {\\rm a.e.,} t\\in[0,T], \\Delta z(t_{i}) =I_{i}(z(t_{i})),and i=1,2,\\ldots,l, z(0)= z(T) = 0,\\end{cases}\\tag{0.1}\\end{align*