On integral representation for solution of generalized Sturm-Liouville equation with discontinuity conditions

Abstract

In this paper, some properties of kernel and integral representation of Jost solution are studied for Sturm-Liouville operator with diffusion potential and discontinuity on the half line.

Series representation for the Jost solution of the Sturm‐Liouville equation in impedance form

“…Levin's representation is one of the most actively used tools in studying With a support from Regional Mathematical Center of the Southern Federal University, Rostov-on-Don, Russia, for Vladislav V. Kravchenko. corresponding direct and inverse spectral and scattering problems. 2,3,5,[12][13][14][15] Levin representations have been studied for different types of Sturm-Liouville equations on the half-line (see, e.g., previous studies [16][17][18][19] ), but in all cases, it is necessary to transform the Sturm-Liouville equation to the Schrödinger equation, through the Liouville transformation. 20 An advantage of the impedance equation is that Liouville's transformation is reduced to a unitary multiplication operator.…”

Existence of Positive Solutions for a Class ofpx,qx-Laplacian Elliptic Systems with

“…Elliptic systems of di erential equations are of crucial importance in modelization and description of a wide variety of phenomena such as uid dynamics, quantum physics, sound, heat, electrostatics, di usion, gravitation, chemistry, biology, simulation of airplane, calculator charts, and time prediction. PDEs are equations involving functions of several variables and their derivatives and model multidimensional systems generalizing ODEs (ordinary di erential equations), which deal with functions of a single variable and their derivatives (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]).…”