42 citations · 126 across the 30 of their papers we have counts for
33 papers
Solvability in the sense of sequences for certain non-Fredholm operators with a drift and Laplace and bi-Laplace operators
Vitali Vougalter
We study the solvability of some linear nonhomogeneous elliptic problems and establish that under certain technical assumptions the convergence in of their right-hand sides y…
Existence of stationary solutions for some systems of integro-differential equations with Laplace and bi-Laplace operators
Vitali Vougalter, Vitaly Volpert
The article is devoted to the solvability of a system of integro-differential equations in the case of the difference of the standard Laplacian and the bi-Laplacian in the diffusio…
Solvability of a class of integro-differential equations with Laplace and bi-Laplace operators
Vitali Vougalter, Vitaly Volpert
The work deals with the studies of the existence of solutions of an integro-differential equation in the situation of the difference of the standard Laplacian and the bi-Laplacian…
On the well-posedness of a certain model with two kernels appearing in the mathematical biology
Messoud Efendiev, Vitali Vougalter
The work is devoted to establishing the global well-posedness in of the integro-differential problem involving the two nonlocal terms describing the di…
Solvability conditions for some non-Fredholm operators with shifted arguments
Vitali Vougalter, Vitaly Volpert
In the first part of the article we establish the existence in the sense of sequences of solutions in for some nonhomogeneous linear differential equation in which one o…
The preservation of nonnegativity of solutions of a parabolic system with the cubed Laplacian
Messoud Efendiev, Vitali Vougalter
The article is devoted to the easily verifiable necessary condition of the preservation of the nonnegativity of the solutions of a system of parabolic equations containing the cube…
Solvability of some integro-differential equations with the bi-Laplacian and transport
Vitali Vougalter
We demonstrate the existence in the sense of sequences of solutions for some integro-differential type problems involving the drift term and the square of the Laplace operator, on…
On the solvability of some systems of quadratic integral equations in dimensions two and three
Vitali Vougalter
The work deals with the existence of solutions of a certain system of quadratic integral equations in H^2(R^d,R^N), d = 2, 3. We demonstrate the existence of a perturbed solution b…
On the existence of stationary solutions for certain systems of integro-differential equations with the double scale anomalous diffusion
Vitali Vougalter, Vitaly Volpert
The work deals with establishing the solvability of a system of integro-differential equations in the situation of the double scale anomalous diffusion. Each equation of such syste…
On the well-posedness of some model with the cubed Laplacian arising in the Mathematical Biology
Messoud Efendiev, Vitali Vougalter
In the article we establish the global well-posedness in W^{1,(6,2)}(R \times R+) of the integro-differential equation containing the cube of the one dimensional Laplacian and the…
On the well-posedness of a certain model with the bi-Laplacian appearing in the Mathematical Biology
Messoud Efendiev, Vitali Vougalter
The work is devoted to the global well-posedness in W^{1, (4, 2)}(R\times R^{+}) of the integro-differential problem involving the square of the one dimensional Laplace operator al…
Persistence of pulses for certain reaction-diffusion equations in dimensions two and three
Vitali Vougalter
We address the persistence under a perturbation of stationary pulse solutions of some reaction-diffusion type equations in dimensions d=2,3 and evaluate the asymptotic approximatio…
Existence of stationary solutions for some integro-differential equations with the double scale anomalous diffusion
Vitali Vougalter, Vitaly Volpert
The paper is devoted to the investigation of the solvability of an integro-differential equation in the case of the double scale anomalous diffusion with a sum of two negative Lapl…
Existence of solutions for some systems of superdiffusive integro-differential equations in population dynamics depending on the natality and mortality rates
Vitali Vougalter
We prove the existence of stationary solutions for some systems of reaction-diffusion type equations with superdiffusion in the corresponding H^2 spaces. Our method is based on the…
Stability and instability of constant stationary solutions to some integro-differential equations
Yuming Chen, Vitali Vougalter
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients…
Solvability of some integro-differential equations with the logarithmic Laplacian
Vitali Vougalter, Vitaly Volpert
We address the existence in the sense of sequences of solutions for a certain integro-differential type problem involving the logarithmic Laplacian. The argument is based on the fi…
On the existence of solutions for a class of systems of integro-differential equations with the logarithmic Laplacian and drift
Yuming Chen, Vitali Vougalter
In this article, we consider a system of integro-differential equations in L^2(R, R^N), which contains the logarithmic Laplacian in the presence of transport terms. The linear oper…
Existence of solutions for a class of integro-differential equations with the logarithmic Laplacian and transport
Yuming Chen, Vitali Vougalter
In this paper, we consider an integro-differential equation in L^2(R), which involves the logarithmic Laplacian in the presence of a drift term. The linear operator associated with…
On the well-posedness of some model arising in the mathematical biology
Messoud Efendiev, Vitali Vougalter
In the article we establish the global well-posedness in W^{1, 2, 2}(R\times R^{+}) of the integro-differential equation in the case of the anomalous diffusion when the one dimensi…
Solvability of a class of systems of quadratic integral equations
Yuming Chen, Vitali Vougalter
The article is devoted to the existence of solutions of a certain system of quadratic integral equations in H^1(R, R^N). We show the existence of a perturbed solution by using a fi…
On the solvability of some systems of integro-differential equations with and without a drift
Messoud Efendiev, Vitali Vougalter
We prove the existence of solutions for some integro-differential systems containing equations with and without the drift terms in the H^2 spaces by virtue of the fixed point techn…
Doubly nonlocal reaction-diffusion equation and the emergence of species
M. Banerjee, V. Vougalter, V. Volpert
The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms correspond…
Arrest of blowup for the 3-D semi-relativistic Schrödinger-Poisson system with pseudo-relativistic diffusion
Walid Abou Salem, Thomas Chen, Vitali Vougalter
We show global well-posedness in energy norm of the semi-relativistic Schrödinger-Poisson system of equations with attractive Coulomb interaction in in the presence…
Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED. II. The spin case
Jean-Marie Barbaroux, Semjon Vugalter
The hydrogen binding energy in the Pauli-Fierz model with the spin Zeeman term is determined up to the order alpha cube, where alpha denotes the fine-structure constant.