Geodesic
On solutions of second order elliptic equations in cylindrical domains
Ufa mathematical journal, Tome 8 (2016) no. 4, pp. 131-143

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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.
Keywords: Neumann boundary value condition, unbounded domain, low order term, asymptotic behavior of solutions, trichotomy of solutions.
Mots-clés : elliptic equation 
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     author = {A. V. Nekludov},
     title = {On  solutions of second order elliptic equations in cylindrical domains},
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     url = {http://geodesic.mathdoc.fr/item/UFA_2016_8_4_a9/}
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A. V. Nekludov. On  solutions of second order elliptic equations in cylindrical domains. Ufa mathematical journal, Tome 8 (2016) no. 4, pp. 131-143. http://geodesic.mathdoc.fr/item/UFA_2016_8_4_a9/