Existence of solution to boundary value problem for impulsive differential equations (Q708617)

The authors deal with the homogeneous Dirichlet problem \[ \begin{aligned} &-(|u'(t)|^{p-2}u'(t))' = f(t,u(t),u'(t)), \\ &\Delta u'(t_i) = I_i(u(t_i)), \quad i = 1,2,\dots,\ell,\\ &u(0) = u(T) = 0, \end{aligned} \] where \(p \geq 2\), \(0 < t_1 < \dots < t_\ell < T\), \(\Delta u'(t_i) = (|u'|^{p-2}u')(t_i^+) - (|u'|^{p-2}u')(t_i^-)\). The existence of a nontrivial solution is obtained using variational and iterative methods.