Solutions and multiple solutions for periodic systems with nonhomogeneous differential operators (Q1030112)

Consider the nonlinear periodic system with nonsmooth potential \[ (\alpha(t,x'(t)))' + \partial j(t,x(t))\ni 0\,\,\text{ a.e. on}\,\, T = [0,b],\quad x(0) = x(b),\,\, x'(0) = x'(b), \tag{1} \] where \((t,y)\to \alpha(t,y)\) is a set-valued map and \(\partial j(t,x)\) is the generalized subdifferential of the generally nonsmooth locally Lipschitz potential function \(j(t,x).\) The solution of (1) is a function \(x\in C^{1}(T,\mathbb{R}^{n})\) such that \(x(0) = x(b), x'(0) = x'(b).\) The author proves an existence theorem to problem (1) and multiplicity results.