Asymptotic behavior of the solutions of the third order nonlinear differential equationsu‴±tσ u n =0u n =0

Abstract

u" ± t" '~ = 0 (*) (**).

Qualitative behavior of solutions of a third order nonlinear differential equation

“…The problem of obtaining sufficient conditions to ensure that all solutions of certain classes of third order nonlinear differential equations are oscillatory, nonoscillatory, or satisfy some type of integrability condition is an important one in the study of qualitative theory of ordinary differential equations. This problem has been the subject of intensive study in the last three decades, and we refer the reader to the monographs of Gregǔs [7] and Kiguradze and Chanturia [11], as well as the papers [2][3][4][5][6][8][9][10][12][13][14][15][16][17] and the references contained therein. By a solution of (E), we mean a function ∈ 3 ([ , ∞)), ≥ 0 , that satisfies (E) on [ , ∞).…”