TY  - JOUR
AB  - We study the solvability of certain linear and nonlinear nonhomogeneous equations in one dimension involving the logarithmic Laplacian and the transport term. In the linear case we show that the convergence in (Formula presented.) of their right sides yields the existence and the convergence in (Formula presented.) of the solutions. We generalize the results obtained in the earlier article of Efendiev and Vougalter [Solvability in the sense of sequences for some non-Fredholm operators with the logarithmic Laplacian. Monatsh Math. 2023] in the non-Fredholm case without the drift. In the nonlinear part of the work we demonstrate that, under the reasonable technical assumptions, the convergence in (Formula presented.) of the integral kernels implies the existence and the convergence in (Formula presented.) of the solutions.
AU  - Efendiyev, M.A.
AU  - Vougalter, V.*
C1  - 70005
C2  - 55357
CY  - 2-4 Park Square, Milton Park, Abingdon Or14 4rn, Oxon, England
SP  - 1-12
TI  - Solvability in the sense of sequences for some linear and nonlinear Fredholm operators with the logarithmic Laplacian.
JO  - Complex Variables
VL  - 33
IS  - 1
PB  - Taylor & Francis Ltd
PY  - 2024
SN  - 0278-1077
ER  - 

TY  - JOUR
AB  - We prove the existence of solutions for some integro-differential systems containing equations with and without drift terms in the (Formula presented.) spaces by virtue of the fixed point technique when the elliptic equations contain second order differential operators with and without Fredholm property, on the whole real line or on a finite interval with periodic boundary conditions. Let us emphasise that the study of the system case is more complicated than of the scalar situation and requires to overcome more cumbersome technicalities.
AU  - Efendiyev, M.A.
AU  - Vougalter, V.*
C1  - 71107
C2  - 55911
CY  - 2-4 Park Square, Milton Park, Abingdon Or14 4rn, Oxon, England
TI  - On the solvability of some systems of integro-differential equations with and without a drift.
JO  - Complex Variables
PB  - Taylor & Francis Ltd
PY  - 2024
SN  - 0278-1077
ER  - 

TY  - JOUR
AB  - 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 terms proportional to the Dirac delta function. The proof of the existence of solutions is based on a fixed point technique. We use the solvability conditions for the non- Fredholm elliptic operators in unbounded domains. We emphasize that the study of the systems is more difficult than of the scalar case and requires to overcome more cumbersome technicalities.
AU  - Efendiyev, M.A.
AU  - Vougalter, V.*
C1  - 68406
C2  - 53646
CY  - 2-4 Park Square, Milton Park, Abingdon Or14 4rn, Oxon, England
TI  - On the solvability of some systems of integro-differential equations with transport and concentrated sources.
JO  - Complex Variables
PB  - Taylor & Francis Ltd
PY  - 2023
SN  - 0278-1077
ER  - 

TY  - JOUR
AU  - Andrievskii, V.V.
C1  - 21706
C2  - 19898
SP  - 35-46
TI  - A Remez-type Inequality in Terms of Capacity.
JO  - Complex Variables
VL  - 45
PY  - 2001
SN  - 0278-1077
ER  -