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