Higher order evolution inequalities involving Leray–Hardy potential singular on the boundary

Article type: Research Article

Authors: Jleli, Mohamed^a | Samet, Bessem^a | Vetro, Calogero^{b; *}

Affiliations: [a] Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia | [b] Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy

Correspondence: [*] Corresponding author. E-mail: calogero.vetro@unipa.it.

Abstract: We consider a higher order (in time) evolution inequality posed in the half ball, under Dirichlet type boundary conditions. The involved elliptic operator is the sum of a Laplace differential operator and a Leray–Hardy potential with a singularity located at the boundary. Using a unified approach, we establish a sharp nonexistence result for the evolution inequalities and hence for the corresponding elliptic inequalities. We also investigate the influence of a nonlinear memory term on the existence of solutions to the Dirichlet problem, without imposing any restrictions on the sign of solutions.

Keywords: Higher order evolution inequalities, Leray–Hardy potential, half ball, nonexistence result

DOI: 10.3233/ASY-231873

Journal: Asymptotic Analysis, vol. 136, no. 3-4, pp. 181-202, 2024