On the univalent solvability of nonlocal problems for an elliptic equation (Q1386554)

This paper deals with the solvability of the following nonlocal problem: \[ \sum^n_{i,j= 1} {\partial\over\partial x_i} \Biggl(a_{ij}(x){\partial u\over\partial x_j}\Biggr)= f(x),\quad x\in Q,\quad u|_{\partial Q}= Bu+ u_0, \] where \(Q\subset\mathbb{R}^n\) and \[ (Bu)(x)= \int_{\overline Q} b(x,y) u(y)dv_x(y). \] {}.