We consider a nonlinear elliptic equation driven by the
$p$-Laplacian and with a Carathéodory right hand side
nonlinearity which exhibits an asymmetric asymptotic behaviour at
$+\infty$ and at $-\infty$.
These hypotheses imply that the Euler functional of the problem
is noncoercive (indefinite). Using critical point theory,
we prove the existence of at least two nontrivial smooth solutions.
Also in the last section for the asymmetric functionals considered here,
we compute the critical groups at infinity.
Publié le : 2010-02-15
Classification:
$p$-Laplacian,
principal eigenvalue,
noncoercive functional,
critical groups,
Poincaré-Hopf formula,
multiple solutions,
35J65,
58E05
@article{1267798500,
author = {Gasi\'nski, Leszek and Papageorgiou, Nikolaos S.},
title = {Multiple Solutions for Noncoercive Problems with the $p$-Laplacian},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {17},
number = {1},
year = {2010},
pages = { 83-99},
language = {en},
url = {http://dml.mathdoc.fr/item/1267798500}
}
Gasiński, Leszek; Papageorgiou, Nikolaos S. Multiple Solutions for Noncoercive Problems with the $p$-Laplacian. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp. 83-99. http://gdmltest.u-ga.fr/item/1267798500/