Solvability of the main boundary value problems for the nonlocal Poisson equation is
studied. Existence and uniqueness theorems for the considered problems are obtained. The …

REPRESENTATION OF THE GREEN’S FUNCTION OF THE EXTERIOR NEUMANN PROBLEM
FOR THE LAPLACE OPERATOR Page 1 Siberian Mathematical Journal, Vol. 58, No. 1, pp …

An explicit representation of the Green's function of the Dirichlet problem for the biharmonic
equation in the unit ball is given. Expansion of the constructed Green's function in the …

In this article we study a generalized third boundary-value problem for homogeneous
biharmonic equation in a unit ball with general boundary operators up to third order …

We show the existence and multiplicity of concentrating solutions to a pure Neumann slightly
supercritical problem in a ball. This is the first existence result for this kind of problem in the …

On Green’s function of the Robin problem for the Poisson equation Skip to content Should
you have institutional access? Here's how to get it ... De Gruyter € EUR - Euro £ GBP - Pound …

We introduce the notion of an elementary solution to the polyharmonic equation and study
its properties. We derive the integral representation for functions in a bounded domain with …

. The coupling mechanisms within the Lane-Emden system differ significantly between these
two cases, resulting in notable variations in solution behaviors. This distinction also leads to …

Abstract The barotropic compressible Navier–Stokes system subject to the Navier-slip
boundary conditions in a general two-dimensional bounded simply connected domain is …

We consider the following slightly supercritical problem for the Lane-Emden system with
Neumann boundary conditions:\begin {equation*}\begin {cases}-\Delta u_1 …