Attarchi, Hassan
Published in
Lobachevskii Journal of Mathematics

AbstractIn this paper, a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3$$\end{document}-Kenmotsu structure is defined on a \documentclass[12pt]{minimal} \usepackage{...

Neverova, D. A.
Published in
Lobachevskii Journal of Mathematics

AbstractThe purpose of this article is to demonstrate with a simple example the complexities that arise when considering boundary-value problems for differential-difference equations. In this paper we discuss in detail smoothness issues of solutions to the Dirichlet problem for linear differential-difference equation with integer shifts. After anal...

Savchuk, A. M. Sadovnichaya, I. V.
Published in
Lobachevskii Journal of Mathematics

AbstractThe paper deals with the Sturm–Liouville operator generated on the finite interval \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0,\pi]$$\end{document} by th...

Faminskii, A. V.
Published in
Lobachevskii Journal of Mathematics

AbstractAn initial-boundary value problem posed on a bounded interval is considered for a class of odd-order (more than one) quasilinear evolution equations with general nonlinearity. Assumptions on the equations do not provide global a priori estimates for solutions of an arbitrary size. For small initial and boundary data, small right-hand side f...

Abasov, N. M.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this article we calculate the order projection in a space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{OA}_{r}(E,F)$$\end{document} of all regula...

Rykhlov, V. S.
Published in
Lobachevskii Journal of Mathematics

AbstractA class of quadratic irregular pencils of the second order ordinary differential operators with constant coefficients is considered in this paper. It is assumed that the boundary conditions are splitting and the characteristic equation has positive roots. Both amounts of two-fold expansions in the series in terms of eigenfunctions of such p...

Solonukha, O. V.
Published in
Lobachevskii Journal of Mathematics

AbstractWe consider the first boundary value problem for quasilinear parabolic differential–difference equations. The uniqueness and existence of generalized solutions are proved. The proofs are based on the theory of linear differential–difference equations and the theory of monotone (pseudomonotone) operators.

Kornuta, A. A. Lukianenko, V. A.
Published in
Lobachevskii Journal of Mathematics

AbstractProblem review of existence and stability nonlinear parabolic functionally differential equations structures with transformation of spatial variables. Such equations model optical systems that contain a thin layer of a nonlinear Kerr-type medium. Review of Initial boundary value problems for circumference, a circle, and a ring with an invol...

Panov, E. Yu.
Published in
Lobachevskii Journal of Mathematics

AbstractWe study the Cauchy problem for nonlinear degenerate parabolic equations with almost periodic initial data. Existence and uniqueness (in the Besicovitch space) of entropy solutions are established. It is demonstrated that the entropy solution remains to be spatially almost periodic and that its spectrum (more precisely, the additive group g...

Pliev, M.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this article we explore orthogonally additive (nonlinear) operators in vector lattices. First we investigate the lateral order on vector lattices and show that with every element \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \us...