On functionals with an infinite number of critical values

In this paper we single out a class of even functional that have an infinite number of critical values that are stable under small perturbations by functional that do not have the property of being even. We give applications to the problem of periodic solutions of a system of ordinary differential equations and to the Dirichlet problem for quasilinear elliptic equations. The basis for the proof of most of the results is made up from the ideas of the method of monotone operators and a variant of the Lyusternik–Shnirel'man theory (cf. RZhMat., 1973, 10B730).
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