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

NGUYEN, Phuoc Tai a Hoang-Hung VO. On the generalized principal eigenvalue of quasilinear operator: definitions and qualitative properties. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. Germany: Springer, 2019, roč. 58, č. 3, s. 1-22. ISSN 0944-2669. Dostupné z: https://dx.doi.org/10.1007/s00526-019-1523-2.

Základní údaje

• Originální název: On the generalized principal eigenvalue of quasilinear operator: definitions and qualitative properties
• Autoři: NGUYEN, Phuoc Tai (704 Vietnam, garant, domácí) a Hoang-Hung VO.
• Vydání: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, Germany, Springer, 2019, 0944-2669.

Další údaje

• Originální jazyk: angličtina
• Typ výsledku: Článek v odborném periodiku
• Obor: 10101 Pure mathematics
• Stát vydavatele: Německo
• Utajení: není předmětem státního či obchodního tajemství
• WWW: URL
• Impakt faktor: Impact factor: 1.526
• Kód RIV: RIV/00216224:14310/19:00113530
• Organizační jednotka: Přírodovědecká fakulta
• Doi: http://dx.doi.org/10.1007/s00526-019-1523-2
• UT WoS: 000468929600003
• Klíčová slova anglicky: ELLIPTIC-OPERATORS; POSITIVE SOLUTIONS; REGULARITY; INEQUALITIES; EXISTENCE; MAXIMUM
• Štítky: rivok
• Příznaky: Mezinárodní význam, Recenzováno

Anotace

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.