Existence and multiplicity results for some scalar fields equations

Abstract

In this paper the results of some researches concerning Scalar Field Equations are summarized. The interest is focused on the question of existence and multiplicity of stationary solutions, so the model equation (Formula presented.) is considered. The difficulties and the ideas introduced to face them as well as some well known results are discussed. Some recent advances concerning existence and multiplicity of multi-bump solutions are described in more detail.