On the Perturbation of Critical Values of Maximum-Minimum Type

In this paper we will deal with critical values of mAYimllm-mininlum type of functionals which arise in the study of boundary value and eigenvalue problems for semilinear elliptic partial differential equations. Our aim is to investigate such critical values under perturbations of the primary functional. In order to explain the basic ideas let X be a real Banach space and let + : X It be a functional having the Fréchet derivative +'. By a critical point of 4' we mean an u € X such that +'(u) = 0; the corresponding value c = +(u) is called a critical value of 4'. The number = sup inf •(u), (1) KEK uEK