Weak solutions in anisotropic (α→(z),β→(z))-Laplacian Kirchhoff models

Résumé fourni par la source

The focus of this research is to establish the existence of infinitely many weak solutions to the double-phase (α→(z),β→(z))-Kirchhoff Neumann problem, characterized by the following equation: {−Φ1(∑i=1N∫Θ1αi(z)|∂φ(z)∂zi|αi(z)dz)Δα→(⋅)φ(z)−Φ2(∑i=1N∫Θ1βi(z)|∂φ(z)∂zi|βi(z)dz)Δβ→(⋅)φ(z)+Φ1(∫Θ1α0(z)|φ(z)|α0(z)dz)|φ(z)|α0(z)−2φ(z)+Φ2(∫Θ1β0(z)|φ(z)|β0(z)dz)|φ(z)|β0(z)−2φ(z)=ψ(z,φ(z))for all z in Θ,∑i=1N|∂φ(z)∂zi|αi(z)−2∂φ(z)∂ziνi=∑i=1N|∂φ(z)∂zi|βi(z)−2∂φ(z)∂ziνi=0on∂Θ. By applying a critical point theorem from B. Ricceri, which is derived from a broader variational framework, we demonstrate that this problem admits infinitely many weak solutions.

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