The authors consider the existence of anti-periodic solutions for differential inclusions in a real Hilbert space .
The first result concerns the problem
is assumed to be an odd maximal monotone mapping, is symmetric and convex, is and satisfies for , for all and , and is a constant such that .
The other theorem concerns the problem
In addition to the hypotheses of the first result, it is assumed that is continuously differentiable and even, maps bounded sets to bounded sets, and is compactly embedded in .
In the case in which is the subdifferential of a lower semi-continuous convex function, the authors obtained similar results as in [Y. Q. Chen, D. O’Regan and J. J. Nieto, Math. Comput. Modelling 46, No. 9–10, 1183–1190 (2007; Zbl 1142.34313)].
The authors conclude the paper by applying the first of these theorems to a boundary value problem for a partial differential equation.