  The Clark theorem is important in critical point theory. For a class of even
functionals it ensures the existence of infinitely many negative critical
values converging to $0$ and it has important applications to sublinear
elliptic problems. We study the convergence of the corresponding critical
points and we give a characterization of accumulation points of critical points
together with examples, in which critical points with negative critical values
converges to non-zero critical point. Our results improve the abstract results
in Kajikiya [Ka1] and Liu-Wang [LW].
