engleski

Rectifiable and unrectifiable oscillations for a generalization of the Riemann-Weber version of Euler differential equation

y '' + 1/x(alpha) {;1/4 + lambda/vertical bar 1nx vertical bar(beta)}; y = 0 on (0, b), b is an element of (0, 1), alpha <= 2, beta > 0, lambda > 0 (for alpha = 2 we suppose that beta = 2 and lambda > 1/4), of the Riemann-Weber version of Euler differential equation is introduced and it is considered together with a suitable boundary layer condition depending on alpha near x = 0. It is shown that this problem is rectifiable (resp., unrectifiable) oscillatory on (0, b) provided alpha is an element of (2, 4) (resp., alpha >= 4). It is a kind of geometrical oscillations on (0, b) for which the finite (resp., infinite) length of the graphs of all its solutions is proposed.

linear equations ; oscillations ; graph ; rectifiability

nije evidentirano