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AGHAJANI, A. RADULESCU, V.
Originální název
Positive supersolutions of non-autonomous quasilinear elliptic equations with mixed reaction
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
angličtina
Originální abstrakt
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.
Klíčová slova
Nonlinear elliptic equation;Liouville theorem;super solution;convection term
Autoři
AGHAJANI, A.; RADULESCU, V.
Vydáno
27. 10. 2023
Nakladatel
Association des Annales de l'Institut Fourier
ISSN
1777-5310
Periodikum
ANNALES DE L INSTITUT FOURIER
Ročník
73
Číslo
6
Stát
Francouzská republika
Strany od
2543
Strany do
2566
Strany počet
24
URL
https://aif.centre-mersenne.org/articles/10.5802/aif.3576/
Plný text v Digitální knihovně
http://hdl.handle.net/11012/245083
BibTex
@article{BUT187372, author="Asodallah {Aghajani} and Vicentiu {Radulescu}", title="Positive supersolutions of non-autonomous quasilinear elliptic equations with mixed reaction", journal="ANNALES DE L INSTITUT FOURIER", year="2023", volume="73", number="6", pages="2543--2566", doi="10.5802/aif.3576", issn="1777-5310", url="https://aif.centre-mersenne.org/articles/10.5802/aif.3576/" }