"Perturbative and variational methods for a class of elliptic equations with critical growth of exponential-type."

Abstract: In this talk, we deal with a class of elliptic PDEs with critical growth of exponential-type. A typical example is represented by the so-called Liouville equation in a planar domain. This type of equations and qualitatively similar ones arise in a broad range of applications and they have attracted great attention over the last decades. Furthermore, if we consider a N-dimensional domain with N>2, in order to preserve the criticality of the problem, we have to replace the Laplacian with the polyharmonic operator for all even dimensions N or with the N-Laplacian. For these types of problems, we show how the presence of topology in the domain strongly implies existence of solutions.