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;