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Journal of Vibration Testing and System Dynamics 10(4) (2026) 353--366 | DOI:10.5890/JVTSD.2026.12.004

Ranis Ibragimov, Svetlin G. Georgiev, Hemanta Kalita

Department of Mathematics, Hampton University, Hampton, VA 23668, USA

Sorbonne University, Paris, France

Mathematics Division, VIT Bhopal University, Bhopal-Indore Highway, Kothrikalan, Sehore, Madhya Pradesh 466114, India

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Abstract

In this paper, we investigate the initial value problem for a two-component Camassa-Holm system (symmetric Keyfitz-Kranzer type model). Under suitable growth conditions, we establish existence of at least one classical solution via fixed-point arguments in a Banach space, existence of at least two nonnegative classical solutions in the positive cone using expansive-contraction methods, and existence of at least three distinct nonnegative classical solutions via coincidence degree theory on annuli. An explicit example has been demonstrated to verify all hypotheses.

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