Geodesic
Estimates of solutions of certain classes of second-order differential
Sbornik. Mathematics, Tome 194 (2003) no. 8, pp. 1113-1123

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Linear second-order differential equations of the form $$ u''(t)+(B+iD)u'(t)+(T+iS)u(t)=0 $$ in a Hilbert space are studied. Under certain conditions on the (generally speaking, unbounded) operators $T$, $S$, $B$ and $D$ the correct solubility of the equation in the “energy” space is proved and best possible (in the general case) estimates of the solutions on the half-axis are obtained. 
@article{SM_2003_194_8_a0,
     author = {N. V. Artamonov},
     title = {Estimates of solutions of certain  classes of  second-order differential},
     journal = {Sbornik. Mathematics},
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     volume = {194},
     number = {8},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_8_a0/}
}
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N. V. Artamonov. Estimates of solutions of certain  classes of  second-order differential. Sbornik. Mathematics, Tome 194 (2003) no. 8, pp. 1113-1123. http://geodesic.mathdoc.fr/item/SM_2003_194_8_a0/