1 - 10 of 16 articles
AbstractLet be an interior mapping of the unit disk, continuous in D2and such that the restriction of f to the unit circle S1 is a locally simple curve γ. Suppose that f(a) ≠ a on S1 and denote by n(a) the number of solutions of the equation f(z) = a in D2, by μ(f) the sum of multiplicities of...
AbstractIn this paper we investigate the existence of mild solutions, on infinite intervals, to initial value problems for neutral functional differential and integrodifferential inclusions in Banach spaces. We shall rely on the fixed point theorem due to Ma, which is an extension on locally...
AbstractIt is proved that if a linear operator l : C([a, b], R) → L ([a, b], R) is nonpositive and for the Cauchy problem u″(t) + l(u)(t) + q(t), u(a) = c the theorem on differential inequalities is valid, then l is a Volterra operator.
AbstractWe prove the boundedness of the Cauchy singular integral operator in special weighted Sobolev and Hölder-Zygmund spaces for large values of the smoothness parameter, which is an integer m ≥ 0, when the underlying contour is piecewise-smooth with angular points and even with cusps. We...
AbstractWe study multidimensional stochastic equationswhere xo is an arbitrary initial state, W is a d-dimensional Wiener process and is a measurable diffusion coefficient. We give sufficient conditions for the existence of weak solutions. Our main result generalizes some results obtained by A....
AbstractWe establish the conditions for the partial moduli of continuity, which guarantee the uniform convergence of N-dimensional trigonometric Fourier series of the functions of the so called generalized partial bounded p-variation.
We establish the conditions for the partial moduli of continuity, which guarantee the uniform convergence of N -dimensional trigonometric Fourier series of the functions of the so called generalized partial bounded p -variation.
AbstractThe existence results obtained for the Dirichlet and mixed BVPs for the equation x ″ = f (t, x, x′) are extended to BVPs with full nonlinear conditions. The proofs are based on the theorem of Granas, Guenther and Lee, while barrier strips are used to obtain a priori bounds for solutions.
AbstractA class of algebraic Poisson structures on R4 is introduced which contains the well-known Sklyanin algebras. For this class, an effective algebraic method of computing Euler characteristics of Casimir levels is developed which enables us to compute them in the case of Sklyanin algebras....
AbstractAn exact solution of the boundary value problems of thermoelastic equilibrium of a homogeneous isotropic rectangular parallelepiped is constructed. The parallelepiped is affected by a stationary thermal field and surface disturbances, in particular, on each side of the rectangular...
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