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- A. ASHYRALYEV, P. E. SOBOLEVSKII
- 2006

The nonlocal boundary value problem for hyperbolic-elliptic equation d2u(t)/dt2 +Au(t) = f (t), (0≤ t ≤ 1), −d2u(t)/dt2 +Au(t) = g(t), (−1≤ t ≤ 0), u(0)= φ, u(1)= u(−1) in a Hilbert space H is considered. The second order of accuracy difference schemes for approximate solutions of this boundary value problem are presented. The stability estimates for the… (More)

- Allaberen Ashyralyev, Yasar Sözen
- Computers & Mathematics with Applications
- 2010

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… (More)

- Ilkay Yaslan Karacaa, Fatma Tokmaka, Allaberen Ashyralyev
- 2014

In this paper, we investigate the existence of double positive solutions for nonlinear third-order m-point boundary value problems with p-Laplacian on time scales. By using double fixed point theorem, we establish results on the existence of two positive solutions with suitable growth conditions imposed on the nonlinear term. As an application, we give an… (More)

- Allaberen Ashyralyev, Elif Ozturk
- Applied Mathematics and Computation
- 2012

Keywords: Elliptic equations Nonlocal boundary value problems Difference schemes Stability a b s t r a c t The well-posedness of the Bitsadze–Samarskii type nonlocal boundary value problem in Hölder spaces with a weight is established. The coercivity inequalities for the solution of the nonlocal boundary value problem for elliptic equations are obtained.… (More)

*Correspondence: aashyr@fatih.edu.tr 1Department of Mathematics, Fatih University, Buyukcekmece, Istanbul, 34500, Turkey 2ITTU, Ashgabat, Turkmenistan Full list of author information is available at the end of the article Abstract In the present paper, a system of nonlinear impulsive differential equations with two-point and integral boundary conditions is… (More)

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 established. The coercivity inequalities for solutions of the boundary value problem for elliptic-parabolic equations are obtained.

The initial-value problem for hyperbolic equation d2u(t)/dt2 +A(t)u(t) = f (t) (0 ≤ t ≤ T), u(0) = φ,u(0) = ψ in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution… (More)

- ALLABEREN ASHYRALYEV, PAVEL E. SOBOLEVSKII
- 2002

We consider the abstract Cauchy problem for differential equation of the hyperbolic type v′′(t) + Av(t) = f (t) (0 ≤ t ≤ T), v(0) = v0, v′(0) = v′ 0 in an arbitrary Hilbert space H with the selfadjoint positive definite operator A. The high order of accuracy two-step difference schemes generated by an exact difference scheme or by the Taylor decomposition… (More)

The abstract nonlocal boundary value problem −d2u t /dt2 Au t g t , 0 < t < 1, du t /dt − Au t f t , 1 < t < 0, u 1 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 Hölder spaces with a weight is established. The coercivity inequalities for the… (More)

- Allaberen Ashyralyev
- Appl. Math. Lett.
- 2009