[PDF][PDF] Linear and nonlinear non-Fredholm operators and their applications

M Efendiev, V Vougalter - Electron. Res. Arch, 2022 - researchgate.net
In this survey we discuss the recent results on the existence in the sense of sequences of
solutions for certain elliptic problems containing the non-Fredholm operators. First of all, we …

Solvability in the sense of sequences for some non-Fredholm operators with the logarithmic Laplacian

M Efendiev, V Vougalter - Monatshefte für Mathematik, 2023 - Springer
We establish the solvability of certain linear nonhomogeneous equations and demonstrate
that under reasonable technical conditions the convergence in L 2 (R d) of their right sides …

Existence of solutions for some systems of integro-differential equations with transport and superdiffusion

M Efendiev, V Vougalter - Analysis and Mathematical Physics, 2022 - Springer
We establish the existence in the sense of sequences of solutions for certain systems of
integro-differential equations which involve the drift terms and the square root of the one …

Solvability in the sense of sequences for some logarithmic Schrödinger operators in higher dimensions

M Efendiev, V Vougalter - Journal of Pseudo-Differential Operators and …, 2023 - Springer
We study the solvability of certain linear nonhomogeneous equations containing the
logarithm of the sum of the two Schrödinger operators in higher dimensions and …

Solvability of some integro-differential equations with drift and superdiffusion

M Efendiev - Linear and Nonlinear Non-Fredholm Operators: Theory …, 2023 - Springer
Solvability of some integro-differential equations with drift and superdiffusion Page 1 Chapter
3 Solvability of some integro-differential equations with drift and superdiffusion In this chapter …

Solvability of some systems of integro-differential equations in population dynamics depending on the natality and mortality rates

V Vougalter, V Volpert - Arnold Mathematical Journal, 2024 - Springer
We establish the existence of stationary solutions for certain systems of reaction–diffusion-
type equations in the corresponding H 2 spaces. Our method relies on the fixed point …

Solvability of some systems of non-Fredholm integro-differential equations with mixed diffusion

M Efendiev, V Vougalter - Journal of Dynamics and Differential Equations, 2024 - Springer
We prove the existence in the sense of sequences of solutions for some system of integro-
differential type equations in two dimensions containing the normal diffusion in one direction …

On the solvability of some systems of integro-differential equations with concentrated sources

V Vougalter, V Volpert - Zeitschrift für angewandte Mathematik und Physik, 2022 - Springer
The article is devoted to the existence of solutions of a system of integro-differential
equations in the case of the normal diffusion and the influx/efflux terms proportional to the …

[PDF][PDF] Solvability of some Fredholm integro-differential equations with mixed diffusion in a square

M Efendiev, V Vougalter - Discrete Contin. Dyn. Syst. Ser. S …, 2024 - kleine.mat.uniroma3.it
We demonstrate the existence in the sense of sequences of solutions for some integro-
differential type problems in a square in two dimensions with periodic boundary conditions …

On the solvability of some systems of integro-differential equations with transport and concentrated sources

M Efendiev, V Vougalter - Complex Variables and Elliptic Equations, 2024 - Taylor & Francis
The article is devoted to the existence of solutions of a system of integro-differential
equations involving the drift terms in the case of the normal diffusion and the influx/efflux …