On some recent variational principles

Abstract

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In this paper we survey some recent variational principies, which have proved to be very useful in the applications to the theory of differential equations, both ordinary and partial. We start with a basic principle due to Ekeland [4}, which provides new proofs to the well known minimax theorems of Ambrosetti - Rabinowitz [2} and Rabinowitz{7}, {8}. For proofs of these results we refer to{8}. We also mention some applications to semilinear elliptic equations.