Remarks on Entire Solutions for Two Fourth-Order Elliptic Problems

DOI10.1017/S0013091515000371zbMath1372.35117arXiv1401.4400OpenAlexW3098533318MaRDI QIDQ2976226

Baishun Lai, Dong Ye

Publication date: 28 April 2017

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.4400

zbMATH Keywords

asymptotic expansionsentire solutionssemi-linear elliptic equationspolyharmonic equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Entire solutions to PDEs (35B08) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (12)

On the sub poly-harmonic property for solutions to \((- \Delta)^p u < 0\) in \(\mathbb{R}^n\) ⋮ Stability for entire radial solutions to the biharmonic equation with negative exponents ⋮ On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents ⋮ A local pointwise inequality for a biharmonic equation with negative exponents ⋮ Radial singular solutions for a fourth order equation with negative exponents ⋮ A pointwise inequality for a biharmonic equation with negative exponent and related problems ⋮ Biharmonic equations with totally characteristic degeneracy ⋮ A perturbed fourth order elliptic equation with negative exponent ⋮ Exhaustive existence and non-existence results for some prototype polyharmonic equations in the whole space ⋮ A critical \(p\)-biharmonic system with negative exponents ⋮ Unnamed Item ⋮ Recent progress on stable and finite Morse index solutions of semilinear elliptic equations

Cites Work

• Ganze Lösungen der Differentialgleichung \(\Delta^p u = f(u)\)
• Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity
• Nonradial solutions for a conformally invariant fourth order equation in \(\mathbb {R}^4\)
• Multiplicity of solutions for a fourth order equation with power-type nonlinearity
• Classification of solutions of higher order conformally invariant equations
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• A note on a class of higher order conformally covariant equations
• Nonlinear biharmonic equations with negative exponents
• The Gel'fand problem for the biharmonic operator

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