Explicit \(L^\infty\)-norm estimates via Morse index for the bi-harmonic and tri-harmonic semilinear problems

DOI10.1007/s00229-018-1037-9zbMath1421.35160OpenAlexW2803659431MaRDI QIDQ1740374

Dong Ye, Abdellaziz Harrabi, Foued Mtiri

Publication date: 30 April 2019

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-018-1037-9

zbMATH Keywords

Dirichlet boundary conditionNavier boundary conditionpolyharmonic elliptic equations

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (4)

\(L^\infty \)-norm estimates of weak solutions via their Morse indices for the \(m\)-Laplacian problems ⋮ A priori estimates for super-linear elliptic equation: the Neumann boundary value problem ⋮ Solutions of super-linear elliptic equations and their Morse indices ⋮ High-order Bahri-Lions Liouville-type theorems

Cites Work

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• A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems
• Nodal sets and Morse indices of solutions of super-linear elliptic PDEs
• Infinite dimensional Morse theory and multiple solution problems
• Morse indices of solutions for super-linear elliptic PDE's
• Existence results and a priori bounds for higher order elliptic equations and systems
• Solutions of superlinear elliptic equations and their morse indices

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