Two-parameter second-order differential inclusions with antiperiodic conditions

Consider in a real Hilbert space [Formula: see text] the antiperiodic problem, denoted as [Formula: see text] a.e. in [Formula: see text] [Formula: see text] where [Formula: see text] is a given time instant, [Formula: see text] [Formula: see text] are two parameters. Here, [Formula: see text] where [Formula: see text] is a proper, convex, lower semicontinuous, and even function, and [Formula: see text] is a continuous with at most linear growth operator. Also, consider the reduced problem, denoted as [Formula: see text] a.e. in [Formula: see text] [Formula: see text] [Formula: see text] and the (algebraic) inclusion, denoted as [Formula: see text] a.e. in [Formula: see text] The following key topics are addressed: (i) The existence of solutions to the previously mentioned problems and inclusion [Formula: see text]; (ii) Establishing sufficient conditions for the uniqueness of solutions to the aforementioned problems, as well as the continuity of the solution to problem [Formula: see text] with respect to [Formula: see text] and [Formula: see text] including approximation results for the solutions of [Formula: see text] and [Formula: see text] (iii) Applications.