Abstract

In continuing from previous papers, where we studied the existence and uniqueness of the global solution and its asymptotic behavior as time t goes to infinity, we now search for a time-periodic weak solution u(t) for the equation whose weak formulation in a Hilbert space H isddt(u,v)+δ(u,v)+αb(u,v)+βa(u,v)+(G(u),v)=(h,v)where: =d/dt; () is the inner product in H; b(u,v), a(u,v) are given forms on subspaces UW, respectively, of H; δ>0, α0, β0 are constants and α+β>0; G is the Gateaux derivative of a convex functional J:VH[0,) for V=U, when α>0 and V=W when α=0, hence β>0; v is a test function in V; h is a given function of t with values in H.Application is given to nonlinear initial-boundary value problems in a bounded domain of Rn.