Electron. J. Diff. Equ., Vol. 2016 (2016), No. 04, pp. 1-8.

Non-existence of periodic solutions to non-autonomous second-order differential equation with discontinuous nonlinearity

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

Abstract:
We consider a second-order differential equation with discontinuous nonlinearity and sinusoidal external influence, and obtain conditions for the non-existence of periodic solutions.

Submitted June 1, 2015. Published January 4, 2016.
Math Subject Classifications: 34A34, 34A36, 34H05, 93C73.
Key Words: Non-autonomous differential equation; discontinuous nonlinearity; periodic solution; non-existence of solutions.

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Alexander M. Kamachkin
Saint Petersburg State University
7-9, University emb.
199034 St. Petersburg, Russia
email: a.kamachkin@spbu.ru
Dmitriy K. Potapov
Saint Petersburg State University
7-9, University emb.
199034 St. Petersburg, Russia
email: d.potapov@spbu.ru
Victoria V. Yevstafyeva
Saint Petersburg State University
7-9, University emb.
199034 St. Petersburg, Russia
email: v.evstafieva@spbu.ru

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