On asymptotic behavior of solutions to Emden-Fowler type higher-order differential equations

For the equation y (n) + |y| sgn y = 0, k > 1, n = 3, 4, existence of oscillatory solutions y = (x∗ − x)h(log(x − x)), α = n k − 1 , x < x ∗ , is proved, where x is an arbitrary point and h is a periodic non-constant function on R. The result on existence of such solutions with a positive periodic non-constant function h on R is formulated for the equation y (n) = |y| sgn y, k > 1, n = 12, 13, 14.