International Journal of Nonlinear Analysis and Applications

Global existence and blow-up results for a nonlinear viscoelastic higher-order p(x)-Laplacian equation

Articles in Press

Document Type : Research Paper

Author

Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

This study aims for the global existence and blow-up of solutions for a class of nonlinear viscoelastic higher-order $p(x)$-Laplacian equations. First, we prove the global existence of solutions in the appropriate range of the variable exponents and next, by using different methods, we prove the blow-up of solutions with positive and negative initial energy. Our results are new, and it is the first time that taken into consideration, extending and improving the earlier results in the literature, such as (Bol. Soc. Mat. Mex.., 2023, https://doi.org/10.1007/s40590-023-00551-x).

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 03 September 2025
  • Receive Date: 16 October 2024
  • Revise Date: 16 November 2024
  • Accept Date: 19 January 2025