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

Abstract

AbstractProperties of solutions of, are studied in the causeuH(t, u)>0 foru≠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 antiderivativesP(i)(t), withP(n)=Q. Several results of this type ensure the non-existence of positive solutions of (I).