Coercive solvability of parabolic differential equations with dependent operators

In the present paper the nonlocal-boundary value problem for the differential equation of parabolic type v ′ (t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 < λ ≤ T in an arbitrary Banach space with the linear positive operators A(t) is considered. The well-posedness of this problem is established in Banach spaces C β,γ 0 (E) of all continuous functions E-valued functions φ(t) on [0, T] satisfying a H¨older condition with a weight (t+τ ) γ . New exact estimates in Holder norms for the solution of three nonlocal-boundary value problems for parabolic equations are obtained.Publisher's Versio

The v-invariant χ2 sequence spaces

In this paper we define v− invariatness of a double sequence space of χ and examine the v− invariatness of the double sequence space of χ. Furthermore, we give duals of double sequence space of χ.Publisher's Versio

Generalized (2+1)−dimensional breaking soliton equation

In this work, a general (2+1)-dimensional breaking soliton equation is investigated. The Hereman’s simplified method is applied to derive multiple soliton solutions, hence to confirm the model integrability.Publisher's Versio

Partial cone metric space and some fixed point theorems

In the present paper, we have proved some convergence properties of a sequence of elements in a partial cone metric space and thereby we have established some fixed point theorems on it.Publisher's Versio

Runs based on discrete order statistics

In the present paper, we study runs based on discrete order statistics. Limit results for the total number of such runs and the length of the longest run are derived.Publisher's Versio

Extensions of Kannan's fixed point results

In this article, we essentially proved some fixed point results for contractive maps type in quasi-pseudometric spaces. The presented theorems are formulated in an asymmetric setting and therefore generalize some existing results in analysis.Publisher's Versio

Application of the generalized clifford-dirac algebra to the proof of the dirac equation fermi-bose duality

The consideration of the bosonic properties of the Dirac equation with arbitrary mass has been continued. As the necessary mathematical tool the structure and different representations of the 29-dimensional extended real Clifford-Dirac algebra (Phys. Lett. A., 2011, v.375, p.2479) are considered briefly. As a next step we use the start from the Foldy-Wouthuysen representation. On the basis of these two ideas the property of Fermi-Bose duality of the Dirac equation with nonzero mass is proved. The proof is given on the three maim examples: bosonic symmetries, bosonic solutions and bosonic conservation laws. It means that Dirac equation can describe not only the fermionic but also the bosonic states.Publisher's Versio

Notes on certain harmonic starlike mappings

Complex-valued harmonic functions that are univalent and sense-preserving in the unit disk D can be written in the form f = h + ¯g, where h and g are analytic in D. We give some inequalities for normalized harmonic functions that are starlike.Publisher's Versio

Energy preserving integration of bi-Ham

The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the long term preservation of the Hamiltonians and Casimir integrals, which is essential in simulating waves and solitons. Dispersive properties of the AVF integrator are investigated for the linearized equations to examine the nonlinear dynamics after discreization.Publisher's Versio

Solvability of iterative systems of three-point boundary value problems

We establish a criterion for the existence of at least one positive solution for the iterative system of three-point boundary value problems by determining the eigenvalues λi, 1 ≤ i ≤ n, using Guo–Krasnosel’skii fixed point theorem.Publisher's Versio