## On a Method for Studying the Asymptotics of Solutions of Odd-Order Differential Equations with Oscillating Coefficients

Published in Mathematical Notes

Published in Mathematical Notes

Published in Mathematical Notes

Abstract The sub-Laplacian plays a key role in CR geometry. In this paper, we investigate eigenvalues of the sub-Laplacian on bounded domains of strictly pseudoconvex CR manifolds, strictly pseudoconvex CR manifolds submersed in Riemannian manifolds. We establish some Levitin–Parnovski-type inequalities and Cheng–Huang–Wei-type inequalities for the...

Published in Mathematical Notes

Abstract For the abstract Euler–Poisson–Darboux equation, boundary-value problems with Dirichlet and Neumann conditions are considered. The criterion for the uniqueness of the solution is established.

Published in Mathematical Notes

Abstract It is known that, among all the differentiable homeomorphic changes of variable, only the functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi_1 (...

Published in Mathematical Notes

Published in Mathematical Notes

Abstract The paper deals with the study of dynamical systems admitting compact attractors, which describe the behavior of trajectories of the system at infinity and play an important role in the qualitative theory of stability of motion. The properties of trajectories of a dynamical system in the attraction domain of the attractors and on the bound...

Published in Mathematical Notes

Abstract A complete description of multipliers of Fourier–Haar series in Lorentz spaces is given. Necessary and sufficient conditions for sequences of complex numbers to belong to the class \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \us...

Published in Mathematical Notes

Abstract The paper refines the currently known estimates of sums of sine series with monotone coefficients, as well as the upper bound for the sum of the cosine series with convex coefficients.

Published in Mathematical Notes

Abstract We prove the existence in rational spaces of distance graphs without short odd cycles whose chromatic number increases exponentially with the dimension of the space.

Published in Mathematical Notes

Abstract The Banach Contraction Mapping Principle has many generalizations and extensions in different directions. Here we define \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{d...