Geodesic
Stability of a~stationary solution of a~system of activator--inhibitor-type equations with a~double-scale internal transition layer
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 2, pp. 269-288

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We study boundary value problems for systems of second-order ordinary differential equations with quasimonotonicity conditions typical of problems of activator–inhibitor type and with solutions containing domains with large gradients. We obtain sufficient conditions for the existence of a stable stationary solution. Using the asymptotic method of differential inequalities, we prove the existence and stability theorems.
Keywords: internal transition layer, method of differential inequalities, upper and lower solutions, asymptotic approximation, quasimonotonicity conditions. 
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     title = {Stability of a~stationary solution of a~system of activator--inhibitor-type equations with a~double-scale internal transition layer},
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N. T. Levashova; D. S. Samsonov. Stability of a~stationary solution of a~system of activator--inhibitor-type equations with a~double-scale internal transition layer. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 2, pp. 269-288. http://geodesic.mathdoc.fr/item/TMF_2023_215_2_a7/