Electronic Journal of Differential Equations,
Vol. 1997(1997), No. 13, pp 1-10.

Title: Multiple positive solutions for equations involving
       critical Sobolev exponent in R^N

Author: C. O. Alves (Univ. Federal da Paraiba, Brazil)

Abstract: This article concerns with the problem 
$$
-{\rm div }(|\nabla u|^{m-2}\nabla u) = 
\lambda h  u^q+u^{m^*-1},\quad{\rm in}\quad R^N\,. 
$$
Using the Ekeland Variational Principle and the
Mountain Pass Theorem, we show the existence of $\lambda ^*>0$ such that
there are at least two non-negative solutions for each $\lambda$ in 
$(0,\lambda ^*)$.


Submitted April 22, 1997. Published August 19, 1997.
Math Subject Classification: 35J20, 35J25.
Key Words: Mountain Pass Theorem; Ekeland Variational Principle.