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<p>For a reaction-diffusion problem with nonlinear singularly perturbed boundary conditions, we prove the existence and examine the stability of periodic solutions possessing boundary layers. Conditions of the asymptotic stability of these solutions in the Lyapunov sense are obtained. The proof is based on the asymptotic method of differential inequalities.</p>

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ON PERIODIC SOLUTIONS WITH A BOUNDARY LAYER IN PROBLEMS WITH NONLINEAR SINGULARLY PERTURBED BOUNDARY CONDITION

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • E. I. Nikulin

摘要

For a reaction-diffusion problem with nonlinear singularly perturbed boundary conditions, we prove the existence and examine the stability of periodic solutions possessing boundary layers. Conditions of the asymptotic stability of these solutions in the Lyapunov sense are obtained. The proof is based on the asymptotic method of differential inequalities.