On Separability of Non-Linear Tri-Harmonic Operators with Matrix Potentials

Faculty Science Year: 2025
Type of Publication: ZU Hosted Pages: 44-50
Authors:
Hany Ahmed Atia Abdelrahman
Journal: WSEAS TRANSACTIONS on MATHEMATICS WSEAS Volume: 24
Keywords : , Separability , Non-Linear Tri-Harmonic Operators with Matrix    
Abstract:
In this research, we explore the separability of the non-linear tri-harmonic form operator: in the case of 𝐴[𝑢] = 𝛥³𝑢(𝑥) + 𝑉(𝑥, 𝑢(𝑥))𝑢(𝑥), 𝑥 ∈ ℝⁿ, in the space 𝐿₂(ℝⁿ)𝑙 with the operator potential 𝑉(𝑥, 𝑢(𝑥)) ∈𝐿₂(ℝⁿ)𝑙 for every 𝑥 ∈ ℝⁿ, where △ is the Laplace operator in ℝⁿ. That is the coercive inequality holds true.
    
     
 
       

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  • Hany Ahmed Atia Abdelrahman, "On separability of non-linear Schrodinger operators with matrix potentials", De Gruyter, 2022 More
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  • Hany Ahmed Atia Abdelrahman, "Separation Problem for Second Order Elliptic Differential Operators on Riemannian Manifolds", Journal of Computational Analysis and Applications, 2015 More

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