On Elliptic Equations in RN with Critical Exponents

Abstract

<p>In this note we use variational arguments –namely Ekeland’s Principle and the Mountain Pass Theorem– to study the equation</p>

<pre>−∆u + α(x)u = λu^q + u^2*−1 in ℝ^N.</pre>

<p>The main concern is overcoming compactness difficulties due both to the unboundedness of the domain ℝ^N , and the presence of the critical exponent 2* = 2N / (N − 2).</p>