Karelin, O., Tarasenko, A. and Gonzalez-Hernandez, M. (2013) Application of Functional Operators with Shift to the Study of Renewable Systems when the reproductive Processed is Describedby Integrals with Degenerate Kernels. Applied Mathematics, 4, 1376-1380.
https://doi.org/10.4236/am.2013.410186

has been cited by the following article:

• TITLE: On Invertibility of Some Functional Operators with Shift

  AUTHORS: Aleksandr Karelin, Anna Tarasenko, Manuel Gonzalez-Hernandez

  KEYWORDS: Operator with a Non-Carlemann Shift, Inverse Operator, Non-Linear Equation, Factorization of Coefficient, Equation with Unit Coefficient

  JOURNAL NAME: Applied Mathematics, Vol.13 No.8, August 19, 2022

  ABSTRACT: In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.