Browsing by Author "Aksoy, U."

Now showing 1 - 6 of 6

Citation - WoS: 4
Citation - Scopus: 7
Dirichlet Problem for a Generalized Inhomogeneous Polyharmonic Equation in an Annular Domain
(Taylor & Francis Ltd, 2012) Aksoy, U.; Celebi, A. O.; Mathematics
In this article, we investigate the solvability of the Dirichlet problems in ring domains for elliptic linear complex partial differential equations having polyharmonic operators as main parts. First, we give higher order Green functions as fundamental solutions of the homogeneous problems using the iteration of harmonic Green functions for ring domains. Second, we introduce some classes of operators related to Dirichlet problems together with their basic properties. Next, we transform the original problems into equivalent singular integral equations. Finally, solvability of the problems is discussed by defining the adjoint problems and using Fredholm alternative.
Citation - WoS: 11
Dirichlet Problems for the Generalized n-poisson Equation
(Birkhauser verlag Ag, 2010) Aksoy, U.; Celebi, A. O.; Mathematics
Polyharmonic hybrid Green functions, obtained by convoluting polyharmonic Green and Almansi Green functions, are taken as kernels to define a hierarchy of integral operators. They are used to investigate the solvability of some types of Dirichlet problems for linear complex partial differential equations with leading term as the polyharmonic operator.
A New Approach To the Existence and Uniqueness of Solutions for A Class of Nonlinear Q-Fractional Boundary Value Problems
(Institute of Applied Mathematics of Baku State University, 2025) Karapinar, E.; Sevinik-Adiguzel, R.; Aksoy, U.; Erhan, I. M.; Mathematics
The object of this study is a boundary value problem associated with a q-difference equation of fractional order. The existence and uniqueness of a solution in the case of multi-point boundary conditions is studied from the viewpoint of fixed point theory. An integral equation equivalent to the boundary value problem is derived and the fixed points of the related integral operator are investigated by using a contractive condition involving a comparison function. The Ulam-Hyers stability of the problem is also discussed. Theoretical results are followed by a particular example.
Citation - WoS: 3
Citation - Scopus: 5
Polyharmonic Robin Problem for Complex Linear Partial Differential Equations
(Taylor & Francis Ltd, 2014) Aksoy, U.; Celebi, A. O.; Mathematics
In this article, generalized polyharmonic Robin functions are introduced together with some of their properties. A hierarchy of integral operators with relevant kernel functions are investigated. These operators are used to transform the Robin problem for a 2nth order linear partial complex differential equation with polyharmonic leading term (generalized n-Poisson equation) into a singular integral equation having Fredholm property.
Citation - WoS: 2
Citation - Scopus: 5
Schwarz problem for higher order linear equations in a polydisc
(Taylor & Francis Ltd, 2017) Aksoy, U.; Celebi, A. O.; Mathematics
In this paper, we discuss the Schwarz boundary value problem for higher order linear complex differential equations in the unit polydisc of C-2. After the relevant preparations, we give the solution for a model equation with homogeneous boundary conditions. Then we obtain the solutions of a linear equation involving Schwarz boundary conditions on the unit polydisc.
Citation - WoS: 13
Citation - Scopus: 15
Schwarz problem for higher-order complex elliptic partial differential equations
(Taylor & Francis Ltd, 2008) Aksoy, U.; Celebi, A. O.; Mathematics
In this paper, we investigate the solvability of a higher order elliptic differential equation with the Schwarz conditions on the unit disc of the complex plane.