Positive Solutions with Nonpower Asymptotic Behavior and Quasiperiodic Solutions to an Emden–Fowler Type Higher Order Equations

Abstract

We consider the differential equation y (n) = p 0|y| k sgn y, where p 0 > 0 and 12 ≤ n ≤ 14, and prove that there exists k > 1 such that the equation has positive solutions with nonpower asymptotics y(x) = (x ∗ -x) -α h(ln (x ∗ -x)), x < x ∗ , where h is a nonconstant continuous positive periodic function. For n ≥ 2 we prove that such a solution exists, but with an oscillating periodic function h. Bibliography: 8 titles. Illustrations: 1 figure.