ASYMPTOTIC ESTIMATE OF SOLUTION OF ONE MIXED DIFFERENCE-DIFFERENTIAL EQUATION OF OSCILLATIONS THEORY

Asymptotic expression of unimprobable estimates of solution of the pro blem <m(sigma)over bar (j)>(t) = c delta(2)sigma(j)(t) (j = 2, ..., N - 1; 0 less than or equal to t < infinity), sigma(0)(t) = F, sigma(N)( t) = 0(0 less than or equal to t < infinity); sigma(j)(0) = 0, sigma(j )(0) = 0 (j = 1, ..., N - 1) are obtained, if j = sN, s is a fixed dya dic, N --> infinity. Here m, c are positive constants, and delta is a symmetric difference operator with respect to j. This problem defines tension forces in the homogeneous chain of N material particles, joint ed in consecutive order with massless springs of linear elasticity.