Positive solutions to the sublinear Lane-Emden equation are isolated

Lorenzo Brasco; Guido De Philippis; Giovanni Franzina

doi:10.1080/03605302.2021.1920613

Positive solutions to the sublinear Lane-Emden equation are isolated

Lorenzo Brasco, Guido De Philippis, Giovanni Franzina

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.

Original language	English (US)
Pages (from-to)	1940-1972
Number of pages	33
Journal	Communications in Partial Differential Equations
Volume	46
Issue number	10
DOIs	https://doi.org/10.1080/03605302.2021.1920613
State	Published - 2021

Keywords

Cone condition
Lane-Emden equation
constrained critical points
eigenvalues

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605302.2021.1920613

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title = "Positive solutions to the sublinear Lane-Emden equation are isolated",

abstract = "We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.",

keywords = "Cone condition, Lane-Emden equation, constrained critical points, eigenvalues",

author = "Lorenzo Brasco and {De Philippis}, Guido and Giovanni Franzina",

note = "Funding Information: Part of this work has been done during some visits of G. D. P. to the University of Bologna and of the three authors to the University of Firenze. The relevant Departments of Mathematics are kindly acknowledged for their hospitality. Publisher Copyright: {\textcopyright} 2021 Taylor & Francis Group, LLC.",

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T1 - Positive solutions to the sublinear Lane-Emden equation are isolated

AU - Brasco, Lorenzo

AU - De Philippis, Guido

AU - Franzina, Giovanni

N1 - Funding Information: Part of this work has been done during some visits of G. D. P. to the University of Bologna and of the three authors to the University of Firenze. The relevant Departments of Mathematics are kindly acknowledged for their hospitality. Publisher Copyright: © 2021 Taylor & Francis Group, LLC.

PY - 2021

Y1 - 2021

N2 - We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.

AB - We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.

KW - Cone condition

KW - Lane-Emden equation

KW - constrained critical points

KW - eigenvalues

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SP - 1940

EP - 1972

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 10

ER -

Positive solutions to the sublinear Lane-Emden equation are isolated

Abstract

Keywords

ASJC Scopus subject areas

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