Geodesic
Condition of completeness of elementary solutions for degenerate higher order operator differential equations
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 12 (2005) no. 1, pp. 86-102 Cet article a éte moissonné depuis la source Math-Net.Ru

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In a Banach space, the higher order abstract differential equation $\sum\limits_{j=0}^nA_ju^{(j)}(t)=0$ is investigated. The operator $A_n$ in the higher derivative may be degenerate. Conditions of approximation of solutions by linear combinations of elementary solutions have been obtained. Abstract results are applied to partial differential equations. 
@article{JMAG_2005_12_1_a4,
     author = {A. L. Piven},
     title = {Condition of completeness of elementary solutions for degenerate higher order operator differential equations},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {86--102},
     year = {2005},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2005_12_1_a4/}
}
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A. L. Piven. Condition of completeness of elementary solutions for degenerate higher order operator differential equations. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 12 (2005) no. 1, pp. 86-102. http://geodesic.mathdoc.fr/item/JMAG_2005_12_1_a4/