Geodesic
On differential equations with nonlocal switch functionals
Contemporary Mathematics. Fundamental Directions, Partial differential equations, Tome 39 (2011), pp. 163-172

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Systems of ordinary differential equations along with nonlocal functionals are considered. These functionals allow us to watch qualitative characteristics of solutions. It is proved that if assumptions are natural, then the switch moment can be found by means of finite difference approximations of differential equations. The results obtained are used to modify the system of equations describing surface waves of an ideal liquid in conformal variables. 
@article{CMFD_2011_39_a9,
     author = {R. V. Shamin},
     title = {On differential equations with nonlocal switch functionals},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {163--172},
     publisher = {mathdoc},
     volume = {39},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2011_39_a9/}
}
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R. V. Shamin. On differential equations with nonlocal switch functionals. Contemporary Mathematics. Fundamental Directions, Partial differential equations, Tome 39 (2011), pp. 163-172. http://geodesic.mathdoc.fr/item/CMFD_2011_39_a9/