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A Wave Inequality with Convolution Nonlinearities

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Abstract

We consider a wave inequality in an exterior domain of \({\mathbb {R}}^{N}\), involving the product of two nonlinear convolution terms. The problem is considered under an inhomogeneous Dirichlet-type boundary condition. We establish sufficient conditions depending on the parameters of the problem, under which we have existence/nonexistence of weak solutions.

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Author Contributions

All authors contributed equally in this paper. All authors reviewed the manuscript.

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Acknowledgements

The authors thank the anonymous referees for their helpful comments that improved the quality of the manuscript. The second author is supported by Researchers Supporting Project number (RSP2023R4), King Saud University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Mohamed Jleli & Bessem Samet

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  1. Mohamed Jleli
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  2. Bessem Samet
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Correspondence to Bessem Samet.

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Jleli, M., Samet, B. A Wave Inequality with Convolution Nonlinearities. Mediterr. J. Math. 20, 328 (2023). https://doi.org/10.1007/s00009-023-02530-y

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  • DOI: https://doi.org/10.1007/s00009-023-02530-y

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