Geodesic
Study of stability of solutions of second order parabolic equations in the critical case
Izvestiya. Mathematics , Tome 3 (1969) no. 6, pp. 1277-1291.

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The stability of the zero solution of a quasilinear periodic parabolic equation is examined. It is proved that the stability of the zero solution in the critical case is entirely determined by the topological index of the zero solution. 
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Yu. S. Kolesov. Study of stability of solutions of second order parabolic equations in the critical case. Izvestiya. Mathematics , Tome 3 (1969) no. 6, pp. 1277-1291. http://geodesic.mathdoc.fr/item/IM2_1969_3_6_a7/

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