Oscillatory properties of nonselfadjoint fourth order differential equations

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1974

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Abstract

This dissertation is a study of the linear homogeneous differential equation (L) (P(t)y')' + qlowered 1y' + qlowered 2y' + r(t)y = 0. The main objective of this investigation is to determine the effect of various disconjugacy conditions on the oscillatory behavior of solutions of (L). By placing certain sign assumptions on qlowered 1, qlowered 2 and r(t) the equation (L) will satisfy a variety of disconjugacy conditions. In this work four such conditions will be considered. In addition, the following properties of solutions will be investigated: (a) Asymptotic behavior (b) Boundedness (c) Representation (d) Essential uniqueness In each case considered (L) will be nonselfadjoint. Many of the results obtained have no analogue for selfadjoint equations.

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