Myshkis A. D.
Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1148-1153
We investigate the problem of the existence of periodic solutions of the problem of oscillations of a diaphragm with friction and pulse feedback in the case where the times of pulse action are determined by a solution of the system.
Ukr. Mat. Zh. - 1985. - 37, № 5. - pp. 581–589
On the asymptotic behaviour of solutions for a class of differential equations of the second order vanishing in infinity
Ukr. Mat. Zh. - 1965. - 17, № 3. - pp. 74-83
Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 119-134
singular integral equation (3) for a single beam and (5) for a grating of beams. A single parabolic beam is discussed in detail. In this case the equation assumes form (10), and its solution is found in the form of a series (11) with undetermined coefficients, which are found by means of an infinite system of linear equations, the coefficients of which are expressed by double Fourier coefficients (14). A rapidly converging iterational method is indicated for finding the latter; the system of equations is also solved by means of rapidly converging iterations. The method may be extended to polynomial beams higher than the second power and on a grating of beams without essen t i a 1 changes.
On the algorithm-of determining the equivalent initial conditions for linear heterogeneous differential equations with constant coefficients
Ukr. Mat. Zh. - 1961. - 13, № 4. - pp. 104-109