Modulo periodic Poisson stable solutions of quasilinear differential equations

M. Akhmet, M. Tleubergenova, A. Zhamanshin

correcthigh confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves existence, uniqueness, Poisson stability, and exponential asymptotic stability for system (11) under (C1)–(C8) by a fixed-point argument on the set B of Poisson-stable functions and Gronwall estimates; the candidate solution proves the same result via a contraction on a sup-norm ball in BC(R,R^n) and then establishes Poisson stability by a direct shift-difference argument using (C3). The technical ingredients and stability rate match the paper; the proofs differ mainly in the choice of function space and how Poisson-stability is obtained.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript soundly proves existence, uniqueness, and exponential stability of a Poisson-stable (MPPS) solution for quasilinear systems with periodic coefficients and Poisson-stable perturbations under standard small-gain-type conditions. The proof strategy (fixed point plus Poisson-shift control) is classical yet carefully adapted; numerical illustrations enhance intuition. Minor typographical and expository improvements would further strengthen clarity.