The Existence Of The Non-extreme Eventually Positive Solutions For The Third Order Quasilinear Differential Equations

In this paper,we will consider the third order quasilinear differential equation (p(t)|u"|α-1u")’+q(t)|u|β-1u=0. where a and β are both positive constants,p,g∈C[α,∞),α>0,and p(t)>0,q(t)>0for t≥α,In the paper,under the conditions0<β<α and0<α<β,we give the necessary and sufficient condition for the existence if non-extreme eventually positive sikutions of the third order quasilinear differential equations.