On the generalized principal eigenvalue of quasilinear operator: definitions and qualitative properties

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00113530" target="_blank" >RIV/00216224:14310/19:00113530 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00526-019-1523-2" target="_blank" >https://doi.org/10.1007/s00526-019-1523-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00526-019-1523-2" target="_blank" >10.1007/s00526-019-1523-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the generalized principal eigenvalue of quasilinear operator: definitions and qualitative properties

Popis výsledku v původním jazyce

The notions of generalized principal eigenvalue for linear second order elliptic operators in general domains introduced by Berestycki et al. (Commun Pure Appl Math 47:47-92, 1994) and Berestycki and Rossi (J Eur Math Soc (JEMS) 8:195-215, 2006, Commun Pure Appl Math 68:1014-1065, 2015) have become a very useful and important tool in analysis of partial differential equations. This motivates us for our study of various concepts of eigenvalue for quasilinear operator of the form KV[u]:=-Delta(p)u+V-u(p-1), u &gt;= 0. This operator is a natural generalization of self-adjoint linear operators. If is a smooth bounded domain, we already proved in Nguyen and Vo (J Funct Anal 269:3120-3146, 2015) that the generalized principal eigenvalue coincides with the (classical) first eigenvalue of KV. Here we investigate the relation between three types of the generalized principal eigenvalue for KV on general smooth domain (possibly unbounded), which plays an important role in the investigation of their limits with respect to the parameters. We also derive a nice simple condition for the simplicity of the generalized principal eigenvalue and the spectrum of KV in RN. To these aims, we employ new ideas to overcome fundamental difficulties originated from the nonlinearity of p-Laplacian. We also discuss applications of the notions by examining some examples.

Název v anglickém jazyce

On the generalized principal eigenvalue of quasilinear operator: definitions and qualitative properties

Popis výsledku anglicky

The notions of generalized principal eigenvalue for linear second order elliptic operators in general domains introduced by Berestycki et al. (Commun Pure Appl Math 47:47-92, 1994) and Berestycki and Rossi (J Eur Math Soc (JEMS) 8:195-215, 2006, Commun Pure Appl Math 68:1014-1065, 2015) have become a very useful and important tool in analysis of partial differential equations. This motivates us for our study of various concepts of eigenvalue for quasilinear operator of the form KV[u]:=-Delta(p)u+V-u(p-1), u &gt;= 0. This operator is a natural generalization of self-adjoint linear operators. If is a smooth bounded domain, we already proved in Nguyen and Vo (J Funct Anal 269:3120-3146, 2015) that the generalized principal eigenvalue coincides with the (classical) first eigenvalue of KV. Here we investigate the relation between three types of the generalized principal eigenvalue for KV on general smooth domain (possibly unbounded), which plays an important role in the investigation of their limits with respect to the parameters. We also derive a nice simple condition for the simplicity of the generalized principal eigenvalue and the spectrum of KV in RN. To these aims, we employ new ideas to overcome fundamental difficulties originated from the nonlinearity of p-Laplacian. We also discuss applications of the notions by examining some examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

ISSN

0944-2669

e-ISSN

—

Svazek periodika

58

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

22

Strana od-do

1-22

Kód UT WoS článku

000468929600003

EID výsledku v databázi Scopus

2-s2.0-85068619071