@article{Alazman2023, 
author = {Ibtehal Alazman and Ibtisam Aldawish and Mohamed Jleli and Bessem Samet},
title = {Hyperbolic inequalities with a Hardy potential singular on the boundary of an annulus},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {5},
pages = {11629-11650},
keywords = {hyperbolic inequalities, Hardy potential, singularities, nonexistence},
url = {https://www.sciopen.com/article/10.3934/math.2023589},
doi = {10.3934/math.2023589},
abstract = {We are concerned with the study of existence and nonexistence of weak solutions for a class of hyperbolic inequalities with a Hardy potential singular on the boundary    ∂      B    1   of the annulus    A  =      {          x      ∈                        R                3            :      1      <              |            x              |            ≤      2        }  , where    ∂      B    1    =      {          x      ∈                        R                3            :              |            x              |            =      1        }  . A singular potential function of the form    (      |    x      |    −  1      )          −      ρ      ,    ρ  ≥  0, is considered in front of the power nonlinearity. Two types of inhomogeneous boundary conditions on    (  0  ,  ∞  )  ×  ∂      B    2  ,    ∂      B    2    =      {          x      ∈                        R                3            :              |            x              |            =      2        }  , are studied: Dirichlet and Neumann. We use a unified approach to show the optimal criteria of Fujita-type for each case.}
}