On the Fredholm and unique solvability of nonlocal elliptic problems in multidimensional domains

A note on unique solvability of the absolute value equation

It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...

Solvability of Nonlocal Fractional Boundary Value Problems

Fredholm Property of General Elliptic Problems

Linear elliptic problems in bounded domains are normally solvable with a finite-dimensional kernel and a finite codimension of the image, that is, satisfy the Fredholm property, if the ellipticity condition, the condition of proper ellipticity and the Lopatinskii condition are satisfied. In the case of unbounded domains these conditions are not sufficient any more. The necessary and sufficient ...

on translation of politeness strategies in dialogues involving female characters in translations and retranslations of novels translated before and after the islamic revolution of iran and their effects on the image of women: a polysystem theory approach

abstract reception environment has considerable effects on accepting a translation. as the expectations of a target culture and its values and needs change throughout history, its criteria for accepting a translation or rejecting it will change accordingly (gentzler, 2001). the expectations of iran, as the reception environment in the present study, have changed after the islamic revolution. i...

Local Solvability and Regularity Results for a Class of Semilinear Elliptic Problems in Nonsmooth Domains

We consider a class of semilinear elliptic problems in twoand three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Fréchet differentiable. Applying ...