Nehari manifold and multiplicity result for elliptic equation involving p-laplacian problems | Zendy

Khaled Ben Ali | Zendy; Abdeljabbar Ghanmi | Zendy

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Nehari manifold and multiplicity result for elliptic equation involving p-laplacian problems

Author(s) -

Khaled Ben Ali,

Abdeljabbar Ghanmi

Publication year - 2017

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) , lambda , omega , combinatorics , mathematics , bounded function , p laplacian , boundary (topology) , physics , mathematical analysis , 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

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