Boundedness of Critical Points in the Symmetric Mountain Pass Lemma

We study the boundedness of critical points obtained by the symmetric mountain pass lemma. We construct three types of functionals, which have an unbounded sequence of critical values. For the first one, the set of all critical points is bounded although the set of critical values is unbounded. The second one has both an unbounded sequence and a bounded sequence of critical points. For the last one, the set of critical points is countably infinite and unbounded.