On the Existence and Behavior of Solution for p(x)-Biharmonic-Type Hyperbolic Equation With Nonlinear Damping and Variable Exponent Source

Billel Gheraibia, Safa M. Mirgani, Nouri Boumaza and Khaled Zennir

Journal of Mathematics, 2025, vol. 2025, 1-11

Abstract: A fourth-order px-biharmonic-type hyperbolic equation with variable-exponent nonlinearities is considered. The global existence of solutions has been obtained by potential well theory and the continuous principle. Qualitative properties related to the stability of the solution of this equation are obtained using the method of the well-known Komornik lemma. The blow-up of solutions with negative initial energy under certain conditions on the parameters of the equation is investigated.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1627715

DOI: 10.1155/jom/1627715

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