Asymptotic properties of nonoscillatory solutions of higher order differential equations

Disfocality and nonoscillatory solutions of nth order differential equations

“…Likewise, the class A in/2i of (E Hi ) and (E iv ) has to be considered separately. In this connection we have q(A 0 ) = 1 for (E") and (E iH ) and q(A [n/2ì ) è 1 for (E Hi ) and (E iv ) [5,7]. Furthermore, employing a procedure similar to the one used to establish the inequality q(A W2i ) ^ 2, we can prove that q(A [n/21 ) ^ 1 [8].…”

“…Then Lemma 1 requires that g ik ~2) > 0, g«-» < 0, g (k) > 0, or g {k ' 2) < 0, gu-» > 0, g {k) < 0, on [97, 00) for some 7] > b 9 according as g > 0 or g < 0 on [7], 00). Hence, as before, for any finite subinterval / of [77, 00) there exists N x such that m > N x implies (29) g m >0,g' m >0, ...,^-1} >0 in(6,Q.…”