Critical point theorems in cones and multiple positive solutions of elliptic problems

We obtain critical point variants of the compression fixed point theorem in cones of Krasnoselskii. Critical points are localized in a set defined by means of two norms. In applications to semilinear elliptic boundary value problems this makes possible the use of local Moser–Harnack inequalities for the estimations from below. Multiple solutions are found for problems with oscillating nonlinearity.