The Nehari Manifold for p-Laplacian Equation with Dirichlet Boundary Condition
Articles
G. A. A. Afrouzi
Mazandaran University, Iran
S. Mahdavi
Mazandaran University, Iran
Z. Naghizadeh
Mazandaran University, Iran
Published 2007-04-25
https://doi.org/10.15388/NA.2007.12.2.14705
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Keywords

the p-Laplacian
variational methods
Nehari manifold
fibrering maps

How to Cite

Afrouzi, G.A.A., Mahdavi, S. and Naghizadeh, Z. (2007) “The Nehari Manifold for p-Laplacian Equation with Dirichlet Boundary Condition”, Nonlinear Analysis: Modelling and Control, 12(2), pp. 143–155. doi:10.15388/NA.2007.12.2.14705.

Abstract

The Nehari manifold for the equation −∆pu(x) = λu(x)|u(x)|p−2b(x)|u(x)|γ−2u(x) for x ∈ Ω together with Dirichlet boundary condition is investigated in the case where 0 < γ < p. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form of tJ(tu) where J is the Euler functional associated with the equation), we discuss how the Nehari manifold changes as λ changes, and show how existence results for positive solutions of the equation are linked to the properties of Nehari manifold.

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