This article is cited in 1 paper

The Bohl index of a homogeneous parabolic inclusion

V. S. Klimov

P. G. Demidov Yaroslavl State University

Abstract: The Bohl index is associated with a one-parameter family of multi-valued maps of elliptic type $\mathscr F(t)$, $0\le t<\infty$. It determines the asymptotic behaviour of solutions of the parabolic inclusion $0\in y'+\mathscr F(t)y$. Our main aim is to obtain lower bounds for the Bohl index. We study the nature of the dependence of solutions of the above inclusion on the initial value and the map $\mathscr F$. We prove that the Bohl index is stable with respect to perturbations that are small on the average.

Keywords: inclusion, homogeneity, stability, multi-valued map, solution.

UDC: 517.956

MSC: 34A60, 34C11, 34C29, 34D05, 35K20

Received: 16.02.2009
Revised: 13.04.2009

DOI: 10.4213/im4088

 English version: Izvestiya: Mathematics, 2011, 75:2, 347–370

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