Positive solutions of fourth order Emden–Fowler type differential equations in the framework of regular variation

The fourth order nonlinear differential equationsequation(A)x(4)+q(t)|x|γsgnx=0,0<γ<1,with regularly varying coefficient q(t) are studied in the framework of regular variation. It is shown that thorough and complete information can be acquired about the existence of all possible regularly varying solutions of (A) and their accurate asymptotic behavior at infinity.