On stable solutions of the fractional Hénon–Lane–Emden equation

DOI10.1142/S021919971650005XzbMath1344.35163arXiv1410.6786OpenAlexW2964099414MaRDI QIDQ3188190

Mostafa Fazly, Wei, Juncheng

Publication date: 17 August 2016

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.6786

zbMATH Keywords

semilinear elliptic equationsentire solutionsfractional Laplacian operatormonotonicity formula

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate elliptic equations (35J70) Higher-order elliptic equations (35J30) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11) Entire solutions to PDEs (35B08)

Related Items (19)

Finite Morse index solutions of the fractional Henon-Lane-Emden equation with Hardy potential ⋮ Classification of stable solutions to a fractional singular elliptic equation with weight ⋮ On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results ⋮ Liouville type theorems for stable solutions of the weighted elliptic system with the advection term: \(p \geq \vartheta >1\) ⋮ A note on positive supersolutions of the fractional Lane-Emden system ⋮ Liouville results for fractional elliptic equations with Hardy potential ⋮ Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry ⋮ On stable and finite Morse index solutions of the nonlocal Hénon-Gelfand-Liouville equation ⋮ Liouville-type theorem for fractional Kirchhoff equations with weights ⋮ A Liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions ⋮ On the loss of maximum principles for higher-order fractional Laplacians ⋮ Liouville type theorems for fractional and higher-order fractional systems ⋮ On weak solutions to a fractional Hardy-Hénon equation. I: Nonexistence ⋮ Liouville type theorems for some fractional elliptic problems ⋮ Recent progress on stable and finite Morse index solutions of semilinear elliptic equations ⋮ The sharp exponent in the study of the nonlocal Hénon equation in \(\mathbb{R}^N\): a Liouville theorem and an existence result ⋮ Liouville type theorems for stable solutions of the weighted fractional Lane-Emden system ⋮ On weak solutions to a fractional Hardy-Hénon equation. II: Existence ⋮ A Liouville-type theorem for fractional elliptic equation with exponential nonlinearity

Cites Work

• Local integration by parts and Pohozaev identities for higher order fractional Laplacians
• Fractional Laplacian in conformal geometry
• Some Liouville theorems for Hénon type elliptic equations
• Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems
• A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem
• Quasilinear Dirichlet problems driven by positive sources
• Insufficiency of the étale Brauer-Manin obstruction: Towards a simply connected example
• Some Theorems Concerning 2-Dimensional Brownian Motion
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth

This page was built for publication: On stable solutions of the fractional Hénon–Lane–Emden equation