Mohamed Laghzal ; Abdelouahed El Khalil ; Abdelfattah Touzani
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A Weighted Eigenvalue Problems Driven by both p(·)-Harmonic and p(·)-Biharmonic Operators
A Weighted Eigenvalue Problems Driven by both p(·)-Harmonic and p(·)-Biharmonic Operators
Authors: Mohamed Laghzal 1; Abdelouahed El Khalil ; Abdelfattah Touzani
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Mohamed Laghzal;Abdelouahed El Khalil;Abdelfattah Touzani
1 University of Sidi Mohamed Ben Abdellah
The existence of at least one non-decreasing sequence of positive eigenvalues for the problem driven by both p(·)-Harmonic and p(·)-biharmonic operatorsΔp(x)2u-Δp(x)u=λw(x)|u|q(x)-2u in Ω, u∈W2,p(⋅)(Ω)∩W0-1,p(⋅)(Ω),is proved by applying a local minimization and the theory of the generalized Lebesgue-Sobolev spaces Lp(·)(Ω) and Wm,p(·)(Ω).