We consider a nonlinear elliptic problem driven by the $p$-Laplacian and depending on
a parameter. The right-hand side nonlinearity is concave, (i.e., $p$-sublinear) near
the origin. For such problems we prove two multiplicity results, one when the
right-hand side nonlinearity is $p$-linear near infinity and the other when it is
$p$-superlinear. Both results show that there exists an open bounded interval such
that the problem has five nontrivial solutions (two positive, two negative and one
nodal), if the parameter is in that interval. We also consider the case when the
parameter is in the right end of the interval.
@article{1270041030,
author = {Hu, Shouchuan and Papageorgiou, Nikolaos S.},
title = {Multiplicity of solutions for parametric $p$-Laplacian equations with nonlinearity
concave near the origin},
journal = {Tohoku Math. J. (2)},
volume = {62},
number = {1},
year = {2010},
pages = { 137-162},
language = {en},
url = {http://dml.mathdoc.fr/item/1270041030}
}
Hu, Shouchuan; Papageorgiou, Nikolaos S. Multiplicity of solutions for parametric $p$-Laplacian equations with nonlinearity
concave near the origin. Tohoku Math. J. (2), Tome 62 (2010) no. 1, pp. 137-162. http://gdmltest.u-ga.fr/item/1270041030/