Supersolutions to nonautonomous Choquard equations in general domains

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2023
Major/Subject
Mcode
Degree programme
Language
en
Pages
Series
Advances in Nonlinear Analysis, Volume 12, issue 1
Abstract
We consider the nonlocal quasilinear elliptic problem: - Δ m u (x) = H (x) ((I α ∗ (Q f (u))) (x)) β g (u (x)) in ω, -{\Delta }_{m}u\left(x)=H\left(x){(\left({I}_{\alpha }∗ \left(Qf\left(u)))\left(x))}^{\beta }g\left(u\left(x))\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega, where ω \Omega is a smooth domain in R N {{\mathbb{R}}}^{N}, β ≥ 0 \beta \ge 0, I α {I}_{\alpha }, 0 < α < N 0\lt \alpha \lt N, stands for the Riesz potential, f, g: [ 0, a) → [ 0, ∞) f,g:\left[0,a)\to \left[0,\infty), 0 < a ≤ ∞ 0\lt a\le \infty, are monotone nondecreasing functions with f (s), g (s) > 0 f\left(s),g\left(s)\gt 0 for s > 0 s\gt 0, and H, Q: ω → R H,Q:\Omega \to {\mathbb{R}} are nonnegative measurable functions. We provide explicit quantitative pointwise estimates on positive weak supersolutions. As an application, we obtain bounds on extremal parameters of the related nonlinear eigenvalue problems in bounded domains for various nonlinearities f f and g g such as e u, (1 + u) p {e}^{u},{\left(1+u)}^{p}, and (1 - u) - p {\left(1-u)}^{-p}, p > 1 p\gt 1. We also discuss the Liouville-type results in unbounded domains.
Description
Publisher Copyright: © 2023 the author(s), published by De Gruyter.
Keywords
eigenvalue problems, Liouville-type theorems, m-Laplace operator, quasilinear elliptic equations
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Citation
Aghajani , A & Kinnunen , J 2023 , ' Supersolutions to nonautonomous Choquard equations in general domains ' , Advances in Nonlinear Analysis , vol. 12 , no. 1 , 20230107 . https://doi.org/10.1515/anona-2023-0107