×

Datko-Perron’s problem for dichotomy of differential equations. (English) Zbl 1374.34230

The paper discusses an important asymptotic property for differential systems: exponential dichotomy, respectively ordinary dichotomy, using Lebesgue spaces. The authors use techniques of Perron type well known in the literature, see for instance [P. Preda et al., Integral Equations Operator Theory 49, No. 3, 405–418 (2004; Zbl 1058.47040); J. Math. Anal. Appl. 388, No. 2, 1090–1106 (2012; Zbl 1242.34114)] and the references there in. As in other articles, where a more general case of nonuniform exponential dichotomy is considered, \((p, q)\) Perron’s condition for dichotomy with \((p, q)\not =(1,\infty)\) implies exponential dichotomy and \((1,\infty)\) Perron’s condition for dichotomy is equivalent with ordinary dichotomy [loc. cit.].

MSC:

34G10 Linear differential equations in abstract spaces
34D09 Dichotomy, trichotomy of solutions to ordinary differential equations
PDFBibTeX XMLCite