Open AccessNehari manifold and multiplicity result for elliptic equation involving p-laplacian problems
Author(s) -
Khaled Ben Ali,
Abdeljabbar Ghanmi
Publication year - 2018
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.v36i4.34078
Subject(s) - nehari manifold , multiplicity (mathematics) , omega , lambda , mathematics , combinatorics , bounded function , p laplacian , boundary (topology) , mathematical analysis , physics , boundary value problem , quantum mechanics , nonlinear system
This article shows the existence and multiplicity of positive solutions of the $p$-Laplacien problem $$\displaystyle -\Delta_{p} u=\frac{1}{p^{\ast}}\frac{\partial F(x,u)}{\partial u} + \lambda a(x)|u|^{q-2}u \quad \mbox{for } x\in\Omega;\quad \quad u=0,\quad \mbox{for } x\in\partial\Omega$$ where $\Omega$ is a bounded open set in $\mathbb{R}^n$ with smooth boundary, $1