Open Access Research

Linear and nonlinear convolution elliptic equations

Veli B Shakhmurov12 and Ismail Ekincioglu3*

Author Affiliations

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

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Boundary Value Problems 2013, 2013:211  doi:10.1186/1687-2770-2013-211

Published: 19 September 2013

Abstract

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 <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/211/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/211/mathml/M1">View MathML</a> spaces. In application, maximal regularity properties of anisotropic elliptic convolution equations are studied.

MSC: 34G10, 45J05, 45K05.

Keywords:
positive operators; Banach-valued spaces; operator-valued multipliers; boundary value problems; convolution equations; nonlinear integro-differential equations