Nonlinear periodic equations driven by a nonhomogeneous differential operator (Q2843777)

The authors study a nonlinear periodic problem on \(\mathbb{R}^1\) driven by a nonhomogeneous differential operator and with a Carathéodory reaction which is (\(p-1\))-linear near \(\pm \infty\). The differential operator incorporates as special cases the scalar \(p\)-Laplacian, the (\(p,q\))-operator and the scalar \(p-\)mean curvature operator. Using variational methods coupled with truncation techniques and the use of critical groups, they show that the problem has at least three nontrivial solutions (one positive, the second negative and the third nodal).