On the generalized principal eigenvalue of quasilinear operator: definitions and qualitative properties
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On the generalized principal eigenvalue of quasilinear operator: definitions and qualitative properties
Original language description
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 >= 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
ISSN
0944-2669
e-ISSN
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Volume of the periodical
58
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
22
Pages from-to
1-22
UT code for WoS article
000468929600003
EID of the result in the Scopus database
2-s2.0-85068619071