Morse‐type information on palais‐smale sequences obtained by min‐max principles

In the context of the min‐max approach to critical point theory, but without the usual compactness assumptions à la Palais‐Smale and the nondegeneracy conditions à la Fredholm, we construct almost critical points with two‐sided estimates on their approximate Morse indices which are arbitrarily close to certain—a priori given—dual sets. This additional topological and analytical information about almost critical sequences can sometimes be crucial in the proof of their convergence and therefore in solving the corresponding variational problem.