Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians

DOI10.1090/tran/8389zbMath1465.35388arXiv1905.04300OpenAlexW3129174468MaRDI QIDQ4992374

Guolin Qin, Wei Dai, Dao-Min Cao

Publication date: 8 June 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.04300

zbMATH Keywords

classification of solutionsconformally invariant equationsnonnegative classical solutionssuper poly-harmonic propertieshigher-order fractional Laplacians

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06) Quasilinear elliptic equations with (p)-Laplacian (35J92) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (16)

Classification of solutions to mixed order conformally invariant systems in \({\mathbb{R}}^2\) ⋮ Classification of nonnegative solutions to static Schrödinger-Hartree-Maxwell system involving the fractional Laplacian ⋮ On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents ⋮ Classification of nonnegative solutions to fractional Schrödinger-Hatree-Maxwell type system ⋮ Classification of solutions to higher fractional order systems ⋮ Well-posedness for a class of pseudodifferential diffusion equations on the torus ⋮ On a super polyharmonic property of a higher-order fractional Laplacian ⋮ Classification of Solutions to Conformally Invariant Systems with Mixed Order and Exponentially Increasing or Nonlocal Nonlinearity ⋮ Liouville type theorems for poly-harmonic Dirichlet problems of Hénon-Hardy type equations on a half space or a ball ⋮ Classification of solutions to several semi-linear polyharmonic equations and fractional equations ⋮ Liouville-type theorems for fractional Hardy-Hénon systems ⋮ Liouville theorems for nonnegative solutions to Hardy-Hénon type system on a half space ⋮ Nonexistence of positive solutions to \(n\)-th order equations in \(\mathbb{R}^n\) ⋮ Classification of Nonnegative Solutions to Static Schrödinger--Hartree--Maxwell Type Equations ⋮ Liouville theorems for fractional and higher-order Hénon–Hardy systems on ℝⁿ ⋮ Classification of nonnegative solutions to Schrödinger equation with logarithmic nonlinearity

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