Multiple and nodal solutions for a class of nonlinear, nonhomogeneous periodic eigenvalue problems (Q347103)

The paper is concerned with a parametric nonlinear periodic problem governed by a non-homogeneous differential operator. The class of differential operators under consideration includes the scalar \(p\)-Laplacian. The author proves that for certain values of the parameter, there exist five nontrivial solutions of the problem, two positive, two negative and one nodal. In addition, the existence of extremal constant sign solutions is also established. The approach relies on variational and monotonicity methods, truncation techniques, and the theory of critical groups.