ABSTRACT
Again, figure 2 shows that uniqueness is lost in case (a) when f < 0, and still prevails in case (b) when f = 0 whereas existence is lost whenever f > 0. This simple example demonstrates that at the failure of condition (12) , not only uniqueness is lost, but there is also the possibility that existence of solutions fails. Let us point out that when E = g2 , the existence depends on the sign of the parameter f. A similar situation has been observed concerning the existence of equilibrium configurations for a non-linear elastic body subjected to a system of applied forces and constrained to lie in a given region [23]. There is also another point which has to be emphasized with regard to figures 1 and 2. It is quite clear that the equilibrium ( minima) states obtained when E < g2 are stable. This is a classical result stating that when uniqueness is prevailing, so does the stability [10]. Now if
we look at figures 1 and 2, it can be clearly seen that the failure of condition (12) may lead (or not) to unstable equilibria.
