Abstract
In critical point theory, Clark's theorem asserts the existence of a sequence of negative critical values tending to 0 for even coercive functionals. We improve Clark's theorem, showing that such a functional has a sequence of critical points tending to 0. Our result also gives more detailed structure of the set of critical points near the origin. An extension of Clark's theorem is also given. Our abstract results are powerful in applications, and thus lead to much stronger results than those in the literature on existence of infinitely many solutions for partially sublinear problems such as elliptic equations and Hamiltonian systems.
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