Detail publikace

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

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/"
}