Well posedness for one class of elliptic equations with drift

Abstract

We studied one class of second-order elliptic equations with intermediate coefficient and proved that the semi-periodic problem on a strip is unique solvable in Hilbert space. We assume that the intermediate coefficient of the equation is continuously differentiable and grows rapidly near infinity, for example, it grows faster than $(|x|+1 ) \ln (|x|+3)$ ( | x | + 1 ) ln ( | x | + 3 ) . However, we do not impose bounds on its derivatives. We believe that the lower-order coefficient is continuous, can be unlimited and change sign.