Electronic Journal of Differential Equations,
Vol. 1996(1996), No. 09, pp. 1-11.

Title: On elliptic equations in $R^N$ with critical exponents

Authors: C.O. Alves (Univ. Fed. Paraiba, Brazil)
 J.V. Goncalves (Univ. Brasilia, Brazil)
 O.H. Miyagaki (Univ. Fed. Vicosa, Brazil)

Abstract: In this note we use variational arguments --namely Ekeland's 
Principle and the Mountain Pass Theorem-- to study the equation 
$$-\Delta u + a(x)u = \lambda u^q + u^{2^*-1} \quad{\rm in\ } R^N\,.$$ 
The main concern is overcoming compactness difficulties due both to the  
unboundedness of the domain $R^N$, and the presence of the 
critical exponent $2^*= 2N/(N-2)$.

Submitted August 7, 1996. Published October 22, 1996.
Math Subject Class.: 35J20, 35K20. 
Key Words: Elliptic equations; unbounded domains; critical exponents; 
           variational methods.