## Supersolutions to nonautonomous Choquard equations in general domains

 dc.contributor Aalto-yliopisto fi dc.contributor Aalto University en dc.contributor.author Aghajani, Asadollah dc.contributor.author Kinnunen, Juha dc.contributor.department Iran University of Science and Technology dc.contributor.department Department of Mathematics and Systems Analysis dc.contributor.department Department of Mathematics and Systems Analysis en dc.date.accessioned 2023-12-11T09:51:41Z dc.date.available 2023-12-11T09:51:41Z dc.date.issued 2023 dc.description Publisher Copyright: © 2023 the author(s), published by De Gruyter. dc.description.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. en dc.description.version Peer reviewed en dc.format.mimetype application/pdf dc.identifier.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 en dc.identifier.doi 10.1515/anona-2023-0107 dc.identifier.issn 2191-9496 dc.identifier.issn 2191-950X dc.identifier.other PURE UUID: ca01a280-1d11-47f4-ad84-bb0b046e1064 dc.identifier.other PURE ITEMURL: https://research.aalto.fi/en/publications/ca01a280-1d11-47f4-ad84-bb0b046e1064 dc.identifier.other PURE LINK: http://www.scopus.com/inward/record.url?scp=85175248406&partnerID=8YFLogxK dc.identifier.other PURE FILEURL: https://research.aalto.fi/files/129181972/SCI_Aghajani_etal_Advances_in_Nonlinear_Analysis_2023.pdf dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/124892 dc.identifier.urn URN:NBN:fi:aalto-202312117260 dc.language.iso en en dc.publisher De Gruyter dc.relation.ispartofseries Advances in Nonlinear Analysis en dc.relation.ispartofseries Volume 12, issue 1 en dc.rights openAccess en dc.subject.keyword eigenvalue problems dc.subject.keyword Liouville-type theorems dc.subject.keyword m-Laplace operator dc.subject.keyword quasilinear elliptic equations dc.title Supersolutions to nonautonomous Choquard equations in general domains en dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi dc.type.version publishedVersion