A periodic boundary value problem for nonlinear differential equation of the second order is studied. Nagumo condition is not assumed on a part of nonlinearity. Existence and multiplicity results are proved using the method of lower and upper solutions. Results are applied to the generalized Liénard oscillator.
The paper deals with the properties of a monotone operator defined on a subset of an ordered Banach space. The structure of the set of fixed points between the minimal and maximal ones is described.