# Remarks on the Clark theorem

## TL;DR

This paper investigates the convergence behavior of critical points in the Clark theorem, providing new characterizations and examples that extend previous abstract results in critical point theory.

## Contribution

It offers improved theoretical insights into the convergence of critical points for even functionals related to the Clark theorem, including new examples and characterizations.

## Key findings

- Critical points with negative critical values can converge to non-zero critical points.
- The paper provides a characterization of accumulation points of critical points.
- Results extend and improve upon previous abstract results by Kajikiya and Liu-Wang.

## Abstract

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].