Geodesic
On the possible rate of decay at infinity of solutions of second order partial differential equations
Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 343-361 Cet article a éte moissonné depuis la source Math-Net.Ru

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For second-order partial differential equations the question of whether they can have solutions decaying superexponentially at infinity is studied. An example is constructed of an equation $\Delta u=q(x)u$ on the plane with bounded coefficients $q$ having a nonzero solution decaying superexponentially. This example provides a negative answer to a familiar question of E. M. Landis. These questions are also studied for hyperbolic and parabolic equations on manifolds. An example is constructed of a parabolic equation having a nonzero solution $u(x,t)$ decaying superexponentially as $t\to\infty$. 
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V. Z. Meshkov. On the possible rate of decay at infinity of solutions of second order partial differential equations. Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 343-361. http://geodesic.mathdoc.fr/item/SM_1992_72_2_a3/

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