Stability of bifurcating periodic solutions of differential inequalities in IR3

A bifurcation problem for the inequality [GRAPHICS] is considered, where K is a closed convex cone in IR3, A(lambda) a real 3 x 3 matrix depending continuously on a real parameter lambda, G a small pert urbation. Small periodic solutions bifurcating at lambda(0) from the branch of trivial solutions are studied. It is proved that these solutions are st able or they are contained in a certain attracting set A(lambda) if they co rrespond to parameters lambda for which the trivial solution is unstable. F urther, unstable solutions exist among them ii they correspond to parameter s for which the trivial solution is stable.