Electronic Journal of Differential Equations,
Vol. 1996(1996), No. 07, pp. 1-12.

Title: Radially Symmetric Solutions for a Class of Critical Exponent 
       Elliptic Problems in $R^N$

Authors: C. O. Alves (Univ. Federal de Paraiba, Brazil)
 D. C. de Morais Filho (Univ. Federal de Paraiba, Brazil)
  M. A. S. Souto (Univ. Federal de Paraiba, Brazil)

Abstract: We give a method for obtaining radially
symmetric solutions for the critical exponent problem
 $$\left\{
  \eqalign{ -\Delta u+a(x)u=& \lambda u^q+u^{2^*-1}{\rm\ in\ } R^N \cr
  u>0{\rm\ and\ }&\int_{R^N}|\nabla u|^2<\infty\cr } \right.
 $$
where, outside a ball centered at the origin, the non-negative function 
$a$ is bounded from below by a positive constant $a_o>0$. We remark that,
differently from the literature, we do not require any conditions on 
$a$ at infinity.

Submitted July 04, 1996. Published August 30, 1996.
Math Subject Classification: 35A05, 35A15 and 35J20.
Key Words: Radial solutions; critical Sobolev  exponents;
           Palais-Smale condition; Mountain Pass Theorem.