Abstract
This paper is concerned with nonexistence results for a class of nonlinear hyperbolic inequalities with a potential function \(V=V(x)\), posed in A, where A is the annulus domain given by \(A=\{x\in \mathbb {R}^N:\, 1<|x|\le 2\}\). Two types of non-homogeneous boundary conditions depending on time and space are investigated: Neumann type boundary condition and Dirichlet type boundary condition. In particular, we investigate the combined effects of the considered boundary conditions, the behavior of the potential function near the boundary and the power nonlinearity, on the nonexistence of solutions. Moreover, in certain special cases, we show that our results are sharp.
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The second author is supported by Researchers Supporting Project number (RSP–2021/4), King Saud University, Riyadh, Saudi Arabia.
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Jleli, M., Samet, B. Nonexistence for nonlinear hyperbolic inequalities in an annulus. Anal.Math.Phys. 12, 90 (2022). https://doi.org/10.1007/s13324-022-00700-x
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DOI: https://doi.org/10.1007/s13324-022-00700-x