Geodesic
Cauchy problem in a~scale of Banach spaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 281 (2013), pp. 7-15

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The concept of quasidifferential operator in a scale of Banach spaces is formulated. A theorem of existence and uniqueness of a solution to the Cauchy problem for the equation with a nonlinear quasidifferential operator is proved. As an example of application of the theorem, the correctness of the nonlinear nonlocal problem of plane-parallel unsteady potential motion of a liquid with free boundary is proved. 
@article{TM_2013_281_a1,
     author = {L. V. Ovsyannikov},
     title = {Cauchy problem in a~scale of {Banach} spaces},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {7--15},
     publisher = {mathdoc},
     volume = {281},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2013_281_a1/}
}
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L. V. Ovsyannikov. Cauchy problem in a~scale of Banach spaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 281 (2013), pp. 7-15. http://geodesic.mathdoc.fr/item/TM_2013_281_a1/