Well posedness for one class of elliptic equations with drift

Kordan Nauryzkhanovich Ospanov

Boundary Value Problems, 2023

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DOI 10.1186/s13661-023-01727-0
Data confidence 70 medium
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Abstract

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.