Electron. J. Diff. Equ., Vol. 2014 (2014), No. 221, pp. 1-6.

Solution to second-order differential equations with discontinuous right-hand side

Alexander M. Kamachkin, Dmitriy K. Potapov, Victoria V. Yevstafyeva

Abstract:
We consider an ordinary differential equation of second order with discontinuous nonlinearity relative to the phase variable. Phase trajectories are studied. We establish a theorem on the existence of a continuum set for nontrivial solutions and the theorem on the boundedness of solutions.

Submitted January 16, 2014. Published October 21, 2014.
Math Subject Classifications: 34A34, 34A36, 34C11, 34C60.
Key Words: Discontinuous nonlinearity; phase trajectories; existence of solutions

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Alexander M. Kamachkin
Saint Petersburg State University
7-9, University emb., 199034 St. Petersburg, Russia
email: akamachkin@mail.ru
Dmitriy K. Potapov
Saint Petersburg State University
7-9, University emb., 199034 St. Petersburg, Russia
email: potapov@apmath.spbu.ru
Victoria V. Yevstafyeva
Saint Petersburg State University
7-9, University emb., 199034 St. Petersburg, Russia
email: vica@apmath.spbu.ru

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