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2021 Uniform a priori estimates for positive solutions of higher order Lane–Emden equations in $\mathbb R^n$
Wei Dai, Thomas Duyckaerts
Publ. Mat. 65(1): 319-333 (2021). DOI: 10.5565/PUBLMAT6512111

Abstract

In this paper we study the existence of uniform a priori estimates for positive solutions to Navier problems of higher order Lane–Emden equations \begin{equation}\label{0-0} (-\Delta)^{m}u(x)=u^{p}(x), \quad x\in\Omega, \end{equation} for all large exponents $p$, where $\Omega\subset\mathbb{R}^{n}$ is a star-shaped or strictly convex bounded domain with $C^{2m-2}$ boundary, $n\geq4$, and $2\leq m\leq\frac{n}{2}$. Our results extend those of previous authors for second order $m=1$ to general higher order cases $m\geq2$.

Funding Statement

W. Dai is supported by the NNSF of China (No. 11971049), the Fundamental Research Funds for the Central Universities, and the State Scholarship Fund of China (No. 201806025011). T. Duyckaerts is supported by the Institut Universitaire de France and the Labex MME-DII.

Citation

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Wei Dai. Thomas Duyckaerts. "Uniform a priori estimates for positive solutions of higher order Lane–Emden equations in $\mathbb R^n$." Publ. Mat. 65 (1) 319 - 333, 2021. https://doi.org/10.5565/PUBLMAT6512111

Information

Received: 4 October 2019; Revised: 20 April 2020; Published: 2021
First available in Project Euclid: 11 December 2020

MathSciNet: MR4185836
Digital Object Identifier: 10.5565/PUBLMAT6512111

Subjects:
Primary: 35B45
Secondary: 35J40 , 35J91

Keywords: blow up , higher order Lane–Emden equations , Navier problems , ‎positive‎ ‎solutions , uniform a priori estimates

Rights: Copyright © 2021 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.65 • No. 1 • 2021
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