About the Nature of the Spectrum of the Periodic Problem for the Heat Equation with a Deviating Argument

Abstract

We study the nature of the spectrum of the periodic problem for the heat equation with a lower-order term and with a deviating argument. A significant influence of the lower-order term on the correct solvability of this problem is found. We obtain a criterion for the strong solvability of the above-mentioned problem.

On the Spectral Properties of a Wave Operator Perturbed by a Lower-Order Term

“…Note that the operator (13)-(14) is a two-dimensional generalization of the operator discussed in [16] - [17], which has found application to singularly perturbed Cauchy problem [18], to the operator of the heat conductivity in [19], and to the ill-posed problems of mathematical physics in [20] - [21], and Volterra problems in [26] - [27].…”

On Square Root of Sturm-Liuville Operator

“…16) where ̅ 0. This last operator (1.15) -(1.16) has been studied in detail in [67], the results of which were used in study of the Gourse problem for wave equation [68] and in solving inverse problems [69][70]. These two spectral problems are special cases of the spectral problem , 0 1 0, | | | | 0, study of which is of undoubted interest in all respects.…”

ABOUT SINGLE OPERATOR METHOD OF SOLUTION OF A SINGULARLY PERTURBED CAUCHY PROBLEM FOR AN ORDINARY DIFFERENTIAL EQUATION n – ORDER

“…With the help of direct calculations, the generality of the obtained recurrent formula is shown, and additional conditions that appeared in the course of research are removed. This work completes a series of studies devoted to the development of a spectral method for solving ill-posed problems [17][18][19][20][21][22][23][24][25].…”