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On elliptic differential and difference problems in a Hilbert space with special type nonlocal conditions
(Maltepe Üniversitesi, 2019) Ashyralyev, Allaberen; Hamad, Ayman
The nonlocal conditions v(0) = v(2?), 2 ?? 0 v(s)ds = 0 were considered by Sobolevskii in [1] for the study of summability of Fourier series in C-norm. Such type conditions are usefull for study of several differential and difference problems with such type nonlocal conditions. In the present paper elliptic differential and difference problems, in a Hilbert space H with the positive definite operator A ? ?I, ? > 0 are investigated. The stability estimates in max norm in one variable for the solutions of these problems are established. Apprlications are presented for several elliptic differential and difference problems with such type nonlocal conditions. Keywords: Elliptic equation, positive operators, Hilbert space, stability, Sobolevskii type nonlocal conditions.