Supersolutions to nonautonomous Choquard equations in general domains

dc.contributorAalto Universityen
dc.contributor.authorAghajani, Asadollah
dc.contributor.authorKinnunen, Juha
dc.contributor.departmentIran University of Science and Technology
dc.contributor.departmentDepartment of Mathematics and Systems Analysis
dc.contributor.departmentDepartment of Mathematics and Systems Analysisen
dc.descriptionPublisher Copyright: © 2023 the author(s), published by De Gruyter.
dc.description.abstractWe 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.versionPeer revieweden
dc.identifier.citationAghajani , A & Kinnunen , J 2023 , ' Supersolutions to nonautonomous Choquard equations in general domains ' , Advances in Nonlinear Analysis , vol. 12 , no. 1 , 20230107 .
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dc.publisherDe Gruyter
dc.relation.ispartofseriesAdvances in Nonlinear Analysisen
dc.relation.ispartofseriesVolume 12, issue 1en
dc.subject.keywordeigenvalue problems
dc.subject.keywordLiouville-type theorems
dc.subject.keywordm-Laplace operator
dc.subject.keywordquasilinear elliptic equations
dc.titleSupersolutions to nonautonomous Choquard equations in general domainsen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi