Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods (Q430286)

The authors consider the impulsive boundary value problem NEWLINE\[NEWLINE \begin{aligned} &-(p(t)u'(t))' + r(t)u'(t) + q(t)u(t) = f(t,u(t)) \, \text{for} \,\, \text{a.e.}\,\, t \in [0,T],\;t \neq t_j,\\ &-\Delta(p(t_j)u'(t_j)) = I_j(u(t_j)), \quad j = 1,\dots,n,\\ & u(0) = 0, a_1u(1) + u'(1) = 0, \end{aligned} NEWLINE\]NEWLINE where \(0 < t_1 < \dots < t_n < 1\), \(f \in C[[0,1]\times{\mathbb R}, {\mathbb R}]\), \(p \in C^1[0,1]\), \(q \in C[0,1]\). There are obtained multiplicity existence results for this type of BVP. As a main tool, variational methods are used.