Linear and nonlinear convolution elliptic equations


Shakhmurov V. B. , Ekincioglu İ.

BOUNDARY VALUE PROBLEMS, vol.2013, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-2770-2013-211
  • Title of Journal : BOUNDARY VALUE PROBLEMS
  • Keywords: positive operators, Banach-valued spaces, operator-valued multipliers, boundary value problems, convolution equations, nonlinear integro-differential equations, BOUNDARY-VALUE-PROBLEMS, FOURIER MULTIPLIER THEOREMS, INTEGRODIFFERENTIAL EQUATIONS, SPACES, REGULARITY, OPERATORS

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 spaces. In application, maximal regularity properties of anisotropic elliptic convolution equations are studied.