# On the fractional Lane-Emden equation

@article{Dupaigne2014OnTF, title={On the fractional Lane-Emden equation}, author={Louis Dupaigne and Juan D{\'a}vila and Juncheng Wei}, journal={Transactions of the American Mathematical Society}, year={2014}, volume={369}, pages={6087-6104} }

We classify solutions of finite Morse index of the fractional Lane-Emden equation (−∆) s u = |u| p−1 u in R n .

#### 52 Citations

Classification of the stable solution to the fractional $2

- Mathematics
- 2016

We classify the stable solutions (positive or sign-changing, radial or not) to the following nonlocal Lane-Emden equation: $(-\Delta)^s u=|u|^{p-1}u$ in $\mathbb{R}^n$ for $2

On stable solutions of the fractional Henon-Lane-Emden equation

- Mathematics
- 2014

We derive monotonicity formulae for solutions of the fractional H\'{e}non-Lane-Emden equation \begin{equation*} (-\Delta)^{s} u=|x|^a |u|^{p-1} u \ \ \ \text{in } \ \ \mathbb{R}^n, \end{equation*}… Expand

On the triharmonic Lane-Emden equation

- Mathematics
- 2016

We derive a monotonicity formula and classify finite Morse index solutions (positive or sign-changing, radial or not) to the following triharmonic Lane-Emden equation: \begin{equation}\nonumber… Expand

On finite Morse index solutions to the quadharmonic Lane-Emden equation

- Mathematics
- 2016

In this paper, we compute the Joseph-Lundgren exponent for the quadharmonic Lane-Emden equation, derive a monotonicity formula and classify the finite Morse index solution to the following… Expand

On finite Morse index solutions of higher order fractional Lane-Emden equations

- Mathematics
- 2014

We classify finite Morse index solutions of the following nonlocal Lane-Emden equation $$(-\Delta)^{s} u=|u|^{p-1} u\quad {\Bbb R}^n$$ for $1<s<2$ via a novel monotonicity formula. For local cases… Expand

Decomposition of polyharmonic operator and classification of homogeneous stable solutions

- Mathematics
- 2021

In this paper, we provide a unified framework to classify homogeneous stable solutions of arbitrary order polyharmonic Lane-Emden equations. The key idea is the spherical decomposition of… Expand

Solutions and Stabilities for a 2D-Non Homogeneous Lane-Emden Fractional System

- Mathematics
- International Journal of Open Problems in Computer Science and Mathematics
- 2018

In this work, we are concerned with a two dimension fractional Lane Emden differential system with right hand side depending on an unknown vector function. Using Banach contraction principle on an… Expand

Monotonicity formulas for extrinsic triharmonic maps and the triharmonic Lane–Emden equation

- Mathematics
- 2017

Abstract We derive monotonicity formulas and e-regularity results for extrinsic triharmonic maps and triharmonic Lane–Emden equations. As an application, we prove partial regularity results for both… Expand

Liouville-type Theorem for Fractional Kirchhoff Equations with Weights

- Mathematics
- 2020

In this paper, we prove a Liouville type theorem for stable solutions to fractional Kirchhoff equations with polynomial nonlinearities and weights.

Recent progress on stable and finite Morse index solutions of semilinear elliptic equations

- Mathematics
- Electronic Research Archive
- 2021

<p style='text-indent:20px;'>We discuss some recent results (mostly from the last decade) on stable and finite Morse index solutions of semilinear elliptic equations, where Norman Dancer has made… Expand

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