Nonlinear periodic systems with the \(p\)-Laplacian: existence and multiplicity results (Q2472080)

The author studies second-order nonlinear periodic systems driven by the vector \(p\)-Laplacian with a nonsmooth, locally Lipschitz potential function. He proves the existence of nontrivial solutions requiring, among others, that the potential function \(j(t,x)\) satisfies a locally, nonuniform anticoercivity. Moreover, she does not assume any polynomial growth of the subdifferential \(\partial j(t,x)\).