Related papers: Existence of solutions for some systems of superdi…
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 diffusion terms. The proof of the existence of solutions is based on…
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 technique when the elliptic equations contain second order…
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 Laplacians in different fractional powers in R^3. The proof of…
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 system involves the sum of the two negative Laplace operators…
In this paper we obtain the existence of a radial solution for some elliptic nonlocal problem with constraints. The problem arises from some reaction-diffusion equation modelling among others system of self-gravitating particles when one…
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 operators associated with the system satisfy the Fredholm…
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 in the diffusion term. The proof of the existence of…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
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 the whole real line or on a finite interval with periodic…
In this paper, we study the local behaviour of solutions near the fixed points of a reaction-diffusion equation with discontinuous nonlinearity. By employing an appropriate linearization around the fixed points, which involves the Dirac…
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 the problem has the Fredholm property. By using a fixed…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
This paper is concerned with the existence of positive solutions for a fractional population model with the homogeneous Dirichlet condition on the exterior of a bounded domain. The approach is based on the sub-super solutions method. Our…
We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially…
We establish several delay-independent criteria for the existence and stability of positive periodic solutions of n-dimensional nonautonomous functional differential equation by several fixed point theorems. Examples from positive and…
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…
We discuss the existence of stationary solutions for logistic diffusion equations of Fisher-Kolmogoroff-Petrovski-Piskunov type driven by the superposition of fractional operators in a bounded region with "hostile" environmental conditions,…
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 fixed point technique when such equation contains the operator…