Nonlocal p-Kirchhoff equations with singular and critical nonlinearity terms

Article type: Research Article

Authors: Ghanmi, Abdeljabbar^a | Kratou, Mouna^b | Saoudi, Kamel^b | Repovš, Dušan D.^{c; *}

Affiliations: [a] Faculté des Sciences de Tunis, LR10ES09 Modélisation Matématique, Analyse Harmonique et Théorie du Potentiel, Université de Tunis El Manar, Tunis 2092, Tunisie | [b] College of Sciences, Imam Abdulrahman Bin Faisal University, 31441 Dammam, Kingdom of Saudi Arabia | [c] Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana & Institute of Mathematics, Physics and Mechanics, 1000 Ljubljana, Slovenia

Correspondence: [*] Corresponding author. E-mail: dusan.repovs@guest.arnes.si.

Abstract: The objective of this work is to investigate a nonlocal problem involving singular and critical nonlinearities: ([u]s,pp)σ−1(−Δ)psu=λuγ+ups∗−1in Ω,u>0,in Ω,u=0,in RN∖Ω, where Ω is a bounded domain in RN with the smooth boundary ∂Ω, 0<s<1<p<∞, N>sp, 1<σ<ps∗/p, with ps∗=NpN−ps, (−Δ)ps is the nonlocal p-Laplace operator and [u]s,p is the Gagliardo p-seminorm. We combine some variational techniques with a truncation argument in order to show the existence and the multiplicity of positive solutions to the above problem.

Keywords: Kirchhoff problem, nonlocal operator, variational methods, singular nonlinearity, multiplicity results

DOI: 10.3233/ASY-221769

Journal: Asymptotic Analysis, vol. 131, no. 1, pp. 125-143, 2023