Electron. J. Diff. Eqns., Vol. 1997(1997), No. 11, pp 1-15.

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

Joao Marcos B. do O

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,

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Joao Marcos B. do O
Universidade Federal da Paraiba
58059.900 Joao Pessoa, Pb Brazil
e-mail: jmbo@mat.ufpb.br

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