Analysis of the effect of certain forcings on the nonoscillatory solutions of even order equations

Abstract Properties of solutions of , are studied in the cause uH(t, u)>0 for u≠0. It is shown that two inequalities may always be associated with (I) in such a way that if one of these inequalities has a small positive solution and the other inequality has a small negative solution, then (I) is oscillatory. Further asymptotic properties of (I) are studied under assumptions involving intermediate antiderivatives P(i)(t), with P(n) = Q. Several results of this type ensure the non-existence of positive solutions of (I).

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