Abstract
When Fournier-Witlem [6] defined the relative topological category ( for a slightly different definition see Fadell [5] ) an objectives was to fred critical points of unbounded potentials. The main result in this direction is the well known AmbrosettiRabinowitz [1] mountain pass theorem. The purpose of this paper is to show that the above can be attained, using the relative category, in the simple cases of some potentials having a disconnected level surface. We also give another proof of the mountain pass theorem and provide a very simple example of application to a differential system of equations. 1. Lusternik-Schnirelman relative category. Let A be a subset of a topological space X. The Lustemik-Schnirelman category of A in X, catx(A), is the least integer n
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