Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


монотонность

On the solvability of a class of nonlinear Hammerstein integral equations on the semiaxis

The paper studies a class of nonlinear integral equations on the semiaxis with a non-compact Hammerstein operator. It is assumed that the kernel of the equation decreases exponentially on the positive part of the number axis. Equations of this kind arise in various fields of natural science. In particular, such equations are found in the theory of radiation transfer in spectral lines, in the mathematical theory of the space-time propagation of an epidemic, in the kinetic theory of gases.

On Solvability of One Class of Urysohn Type Nonlinear Integral Equation on the Whole Line

In present work one class of Urysohn type nonlinear integral equation on whole line is studied. Equations observed have applications in various fields of mathematical physics. It is assumed that Hammerstein type nonlinear integral operator with a difference kernel serves local minorant in terms of M. A. Krasnoselskii for the Urysohn initial operator.

The Solvability of a System of Nonlinear Integral Equations of Hammerstein Type on the Whole Line

In recent years, the interest has grown in nonlinear integral equations of convolution type in connection with their application in various fields of mathematical physics, inparticular, inthep-adic theory of an open-closed string, kinetic theory of gases, in the theory of radiation transfer in spectral lines. The paper is devoted to the questions of construction of nontrivial solutions and the study of their asymptotic behavior for one system of nonlinear integral equations of convolution type with a symmetric kernel on the whole axis.