Existence and stability properties of entire solutions to the polyharmonic equation \((-\Delta)^{m}u=e^{u}\) for any \(m\geq 1\)
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Publication:252568
DOI10.1016/j.anihpc.2014.11.005zbMath1336.35033arXiv1403.0729OpenAlexW2086935404MaRDI QIDQ252568
Alberto Ferrero, Alberto Farina
Publication date: 3 March 2016
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1403.0729
Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Higher-order elliptic equations (35J30) Semilinear elliptic equations (35J61) Entire solutions to PDEs (35B08)
Related Items (8)
On the sub poly-harmonic property for solutions to \((- \Delta)^p u < 0\) in \(\mathbb{R}^n\) ⋮ On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents ⋮ Classification of radial solutions to \(-\Delta_g u = e^u\) on Riemannian models ⋮ Exhaustive existence and non-existence results for some prototype polyharmonic equations in the whole space ⋮ Conformal metrics in \(\mathbb {R}^{2m}\) with constant \(Q\)-curvature and arbitrary volume ⋮ Existence of stable solutions to \((-\Delta)^m u = e^u\) in \(\mathbb{R}^N\) with \(m\geq 3\) and \(N>2m\) ⋮ Higher order conformally invariant equations in \( \mathbb{R}^3 \) with prescribed volume ⋮ Qualitative properties of Hénon type equations with exponential nonlinearity
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