Alexander M. Kamachkin, Dmitriy K. Potapov, Victoria V. Yevstafyeva
Abstract:
We consider an ordinary differential equation of second order with
constant coefficients and a discontinuous right-hand side.
First we use the point mapping method defining first return functions,
then we use the phase-plane method.
We establish both the existence and non-existence of periodic solutions
(including stable ones) and oscillatory solutions depending on the
coefficients of the equation.
By the variational method, we prove the existence of nonzero
semiregular solutions for a boundary-value problem.
Submitted March 15, 2016. Published May 16, 2016.
Math Subject Classifications: 34A34, 34A36, 34C25, 34B15.
Key Words: Point mapping method; first return function; phase-plane method;
periodic solution; stability; variational method; semiregular solution.
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Alexander M. Kamachkin Saint Petersburg State University 7/9, Universitetskaya nab. St. Petersburg, 199034, Russia email: a.kamachkin@spbu.ru |
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Dmitriy K. Potapov Saint Petersburg State University 7/9, Universitetskaya nab. St. Petersburg, 199034, Russia email: d.potapov@spbu.ru |
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Victoria V. Yevstafyeva Saint Petersburg State University 7/9, Universitetskaya nab. St. Petersburg, 199034, Russia email: v.evstafieva@spbu.ru |
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