Positive supersolutions of non-autonomous quasilinear elliptic equations with mixed reaction

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F23%3APU150378" target="_blank" >RIV/00216305:26220/23:PU150378 - isvavai.cz</a>

Result on the web

<a href="https://aif.centre-mersenne.org/articles/10.5802/aif.3576/" target="_blank" >https://aif.centre-mersenne.org/articles/10.5802/aif.3576/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5802/aif.3576" target="_blank" >10.5802/aif.3576</a>

Result language

angličtina

Original language name

Positive supersolutions of non-autonomous quasilinear elliptic equations with mixed reaction

Original language description

We provide a simple method for obtaining new Liouville-type theorems for positive supersolutions of the We We provide a simple method for obtaining new Liouville-type theorems for positive supersolutions of the elliptic problem - Delta(p)u+ b(x)vertical bar del u vertical bar(pq/q+1) = c(x)u(q) in Omega, where Omega is an exterior domain in R-N with N >= p > 1 and q >= p - 1. In the case q not equal p - 1, we mainly deal with potentials of the type b(x) = vertical bar x vertical bar(a), c(x) = lambda vertical bar x vertical bar(sigma), where lambda > 0 and a, sigma is an element of R. We show that positive supersolutions do not exist in some ranges of the parameters p, q, a, sigma, which turn out to be optimal. When q = p - 1, we consider the above problem with general weights b(x) >= 0, c(x) > 0 and we assume that c(x)- b(p)(x)/p(p) > 0 for large vertical bar x vertical bar, but we also allow the case lim(vertical bar x vertical bar ->infinity)[c(x)- b(p)(x)/p(p)] = 0. The weights b and c are allowed to be unbounded. We prove that if this equation has a positive supersolution, then the potentials must satisfy a related differential inequality not depending on the supersolution. We also establish sufficient conditions for the nonexistence of positive supersolutions in relationship with the values of tau := lim sup(vertical bar x vertical bar ->infinity) vertical bar x vertical bar b(x) <= infinity. A key ingredient in the proofs is a generalized Hardy-type inequality associated to the p-Laplace operator.

Czech name

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Czech description

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Type

J_imp - 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

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Name of the periodical

ANNALES DE L INSTITUT FOURIER

ISSN

1777-5310

e-ISSN

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Volume of the periodical

73

Issue of the periodical within the volume

6

Country of publishing house

FR - FRANCE

Number of pages

24

Pages from-to

2543-2566

UT code for WoS article

001109332400001

EID of the result in the Scopus database

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