A system of wave inequalities with inverse-square potentials in an exterior domain

ABSTRACT

We study the existence and nonexistence of solutions to a system of wave inequalities with inverse-square potentials in an exterior domain of ${\mathbb{R}}^N$, under inhomogeneous Dirichlet-type boundary conditions. Our study yields naturally existence and nonexistence results for the corresponding stationary wave system.

KEYWORDS:

• Wave inequalities
• Hardy potential
• exterior domain
• existence
• nonexistence

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35L71
• 35A01
• 35B44
• 35B33

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors are supported by Researchers Supporting Project number (RSP2023R4), King Saud University, Riyadh, Saudi Arabia.