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.