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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)

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)

- Allaberen Ashyralyev, Pavel E Sobolevski ˘ I
- 2005

It is well known the differential equation −u (t) + Au(t) = f (t) (−∞ < t < ∞) in a general Banach space E with the positive operator A is ill-posed in the Banach space C(E) = C((−∞,∞),E) of the bounded continuous functions ϕ(t) defined on the whole real line with norm ϕ C(E) = sup −∞<t<∞ ϕ(t) E. In the present paper we consider the high order of accuracy… (More)

- Allaberen Ashyralyev, Okan Gercek, Yong Zhou
- 2008

The abstract nonlocal boundary value problem −d 2 ut/dt 2 Aut gt, 0 < t < 1, dut/dt − Aut ft, 1 < t < 0, u1 u−1 μ for differential equations in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in H ¨ older spaces with a weight is established. The coercivity inequalities for the solution… (More)