On Elliptic Equations in RN with Critical Exponents

Abstract

In this note we use variational arguments –namely Ekeland’s Principle and the Mountain Pass Theorem– to study the equation −∆u + a(x)u = λuq + u2∗−1 in RN . The main concern is overcoming compactness difficulties due both to the unboundedness of the domain RN , and the presence of the critical expo- nent 2∗ = 2N/(N − 2).