AbstractA bifurcation problem for the inequality\documentclass{article}\pagestyle{empty}\begin{document}$$\left\{ {\begin{array}{*{20}c} {U\left( t \right) \in K,} \\ {\left( {U\left( t \right) - A_\lambda U\left( t \right) - G\left( {\lambda,U\left( t \right)} \right),V - U\left( t \right)} \right) \ge 0\;{\rm{for}}\;{\rm{all}}\;V \in K,\;{\rm{a}}{\rm{.a}}{\rm{.}}\;t \in \left[ {0,T} \right]} \\ \end{array}} \right.$$\end{document}, is considered, whereKis a closed convex cone in IR3,Aλa real 3×3 matrix depending continuously on a real parameter λ,Ga small perturbation. Small periodic solutions bifurcating at λ0from the branch of trivial solutions are studied. It is proved that these solutions are stable or they are contained in a certain attracting set Aλif they correspond to parameters λ for which the trivial solution is unstable. Further, unstable solutions exist among them if they correspond to parameters for which the trivial solution is s