Electronic Journal of Differential Equations,
Vol. 1997(1997), No. 11, pp 1-15.

Title: Solutions to perturbed eigenvalue problems of the p-Laplacian in
       ${\Bbb R}^N$

Author: Joao Marcos B. do O (Univ. Federal da Paraiba, Brazil)

Abstract:
Using a variational approach, we investigate the existence of solutions 
for  non-autonomous perturbations of the 
p-Laplacian eigenvalue problem 
$$
 -\Delta _pu=f(x,u)\quad {\rm in}\quad {\Bbb R}^N\,. 
$$
Under the assumptions that the primitive $F(x,u)$ of $f(x,u)$
interacts only with the first eigenvalue, we look for solutions in
the space $D^{1,p}({\Bbb R}^N)$. 
Furthermore, we assume a condition that measures how different the 
behavior  of the function $F(x,u)$ is from that of the $p$-power of $u$.

Submitted January 24, 1997. Published July 15, 1997.
Math Subject Classification:  35A15, 35J60.
Key Words: Mountain Pass Theorem; Palais-Smale Condition; First eigenvalue;