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Vol 53, No 5 (2018)
- Year: 2018
- Articles: 7
- URL: https://journals.rcsi.science/1068-3623/issue/view/14091
Differential Equations
On the Solvability of a Mixed Problem for an One-dimensional Semilinear Wave Equation with a Nonlinear Boundary Condition
Abstract
In this paper, for an one-dimensional semilinear wave equation we study a mixed problem with a nonlinear boundary condition. The questions of uniqueness and existence of global and blow-up solutions of this problem are investigated, depending on the nonlinearity nature appearing both in the equation and in the boundary condition.
247-259
Meromorphic Solutions for a Class of Differential Equations and Their Applications
Abstract
In this note, we study the admissible meromorphic solutions for algebraic differential equation fnf' + Pn−1(f) = R(z)eα(z), where Pn−1(f) is a differential polynomial in f of degree ≤ n − 1 with small function coefficients, R is a non-vanishing small function of f, and α is an entire function. We show that this equation does not possess any meromorphic solution f(z) satisfying N(r, f) = S(r, f) unless Pn−1(f) ≡ 0. Using this result, we generalize a well-known result by Hayman.
260-265
Functional Analysis
Eigenfunctions of Composition Operators on Bloch-type Spaces
Abstract
Suppose φ is a holomorphic self map of the unit disk and Cφ is a composition operator with symbol φ that fixes the origin and 0 < |φ'(0)| < 1. This paper explores sufficient conditions that ensure all the holomorphic solutions of Schröder equation for the composition operator Cφ to belong to a Bloch-type space Bα for some α > 0. In the second part of the paper, the results obtained for composition operators are extended to the case of weighted composition operators.
266-275
Real and Complex Analysis
276-280
Almost Everywhere Convergence of Strong Nörlund Logarithmic Means of Walsh-Fourier Series
Abstract
In this paper we study the maximal operator for a class of subsequences of strong Nörlund logarithmic means of Walsh-Fourier series. For such a class we prove the almost everywhere strong summability for every integrable function f.
281-287
Conjugate Functions and the Modulus of Smoothness of Fractional Order
Abstract
In the present paper, estimates of the partial moduli of smoothness of fractional order of the conjugate functions of several variables are obtained in the space C(Tn). The accuracy of the obtained estimates is established by appropriate examples.
288-293
On the Convergence of Partial Sums with Respect to Vilenkin System on the Martingale Hardy Spaces
Abstract
In this paper, we derive characterizations of boundedness of subsequences of partial sums with respect to Vilenkin system on the martingale Hardy spaces Hp when 0 < p < 1. Moreover, we find necessary and sufficient conditions for the modulus of continuity of martingales f ∈ Hp, which provide convergence of subsequences of partial sums on the martingale Hardy spaces Hp. It is also proved that these results are the best possible in a special sense. As applications, some known and new results are pointed out.
294-306