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Article Citation - WoS: 2Citation - Scopus: 5Schwarz problem for higher order linear equations in a polydisc(Taylor & Francis Ltd, 2017) Aksoy, U.; Celebi, A. O.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.Article Citation - WoS: 3Citation - Scopus: 5Polyharmonic Robin Problem for Complex Linear Partial Differential Equations(Taylor & Francis Ltd, 2014) Aksoy, U.; Celebi, A. O.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.Article Citation - WoS: 6Citation - Scopus: 9Dirichlet Problem for a Generalized Inhomogeneous Polyharmonic Equation in an Annular Domain(Taylor & Francis Ltd, 2012) Aksoy, U.; Celebi, A. O.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.
