Article
Ufa Mathematical Journal
Volume 8, Number 4, pp. 131-143
On solutions of second order elliptic equations in cylindrical domains
Neklyudov A.V.
DOI:10.13108/2016-8-4-131
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In a semi-infinite cylinder, we consider a second order elliptic equation with a lower order term. On the lateral boundary of the cylinder we impose the homogeneous Neumann condition. We show that each bounded solution tends to a constant at infinity and once the lower order term does not decay too fast, this constant vanishes. We establish that for a sufficiently fast decay of the lower order term, we have a trichotomy of the solutions as for the equation without the lower order term: the solution tends to a general non-zero constant or grows linearly or grows exponentially. The decay conditions for the lower order term are formulated in an integral form.