A variational convergence problem with antiperiodic boundary conditions C. Castaing * T. Haddad † and A. Salvadori ‡ Pacific Journal of Optimization, Vol 6, No 1, pp. 153-176, January 2010 Abstract. We present a variational convergence approach involving exis- tence of solutions for some classes of evolution inclusions with anti-periodic boundary conditions. Mathematics Subject Classifications (2000): 45N05, 47J25, 35B40, 35K55, 35K90. Key words: Anti-periodic, chain rule, maximal monotone, recession, sec- ond dual, subdifferential, Young measures. 1 Introduction Existence and uniqueness of antiperiodic solution for evolution inclusions generated by the subdifferential of a convex lower semicontinuous even func- tion appeared in a series of papers, see [2, 3, 4, 9, 15, 17, 21, 22] and the references therein. In this paper, we present two epigraphical versions of the mentionned results involving new variational convergence techniques and the stable convergence of Young measures [11]. In section 2, we summarize some basic results of convergence for bounded sequences in L 1 H ([0,T ]) where H is a separable Hilbert space. In section 3 we state some existence and * D´ epartement de Math´ ematiques, Universit´ e Montpellier II, 34095 Montpellier Cedex 5, France. E-Mail: castaing.charles@numericable.fr † Faculty of Sciences, Universit´ e de Jijel, Algerie. Email: haddadtr2000@yahoo.fr ‡ Dipartimento di Matematica, Universitet` a Perugia, via Vanvitelli 1, 06123 Perugia, Italia. Email: mateas@unipg.it 1