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.