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The abstract nonlocal boundary value problem − d 2 u(t) dt 2 + sign(t)Au(t) = g(t), (0 ≤ t ≤ 1), du(t) dt + sign(t)Au(t) = f (t), (−1 ≤ t ≤ 0), u(1) = u(−1) + µ for the differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Hölder spaces without a weight is… (More)

The stable difference scheme for the approximate solution of the initial value problem () () () () 1 2 , t du t D u t Au t f t dt + + = () 0 1, 0 0 t u < < = for the differential equation in a Banach space E with the strongly positive operator A and fractional operator 1 2 t D is presented. The well-posedness of the difference scheme in difference analogues… (More)

- Allaberen Ashyralyev, Necmettin Aggez
- TheScientificWorldJournal
- 2014

We are interested in studying multidimensional hyperbolic equations with nonlocal integral and Neumann or nonclassical conditions. For the approximate solution of this problem first and second order of accuracy difference schemes are presented. Stability estimates for the solution of these difference schemes are established. Some numerical examples… (More)

- Allaberen Ashyralyev, Asker Hanalyev
- TheScientificWorldJournal
- 2014

The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 < λ ≤ T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C 0 (β,γ) (E α-β ) of all E α-β -valued continuous… (More)