Linear and nonlinear convolution elliptic equations
1 Department of Mechanical Engineering, Okan University, Tuzla, Istanbul, Turkey
2 Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
3 Department of Mathematics, Dumlupınar University, Kütahya, Turkey
Boundary Value Problems 2013, 2013:211 doi:10.1186/1687-2770-2013-211Published: 19 September 2013
In this paper, the separability properties of elliptic convolution operator equations are investigated. It is obtained that the corresponding convolution-elliptic operator is positive and also is a generator of an analytic semigroup. By using these results, the existence and uniqueness of maximal regular solution of the nonlinear convolution equation is obtained in spaces. In application, maximal regularity properties of anisotropic elliptic convolution equations are studied.
MSC: 34G10, 45J05, 45K05.