Authors: Mohamed Laghzal ¹; 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).

• 35J35 - Variational methods for higher-order elliptic equations
• 47J10 - Nonlinear spectral theory, nonlinear eigenvalue problems
• 58E05 - Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces