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Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 103-109).

We introduce the notion of differential sequences generated by generators of sequences. We discuss the Riccati sequence in terms of symmetry analysis, singularity analysis and identification of the complete symmetry group for each member of the sequence. We provide their invariants and first integrals. We propose a generalisation of the Riccati sequence and investigate its properties in terms of singularity analysis. We find that the coefficients of the leading-order terms and the resonances obey certain structural rules. We also demonstrate the uniqueness of the Riccati sequence up to an equivalence class. We discuss the properties of the differential sequence based upon the equation ww''−2w12 = 0 in terms of symmetry and singularity analyses. The alternate sequence is also discussed. When we analyse the generalised equation ww'' − (1 − c)w12 = 0, we find that the symmetry properties of the generalised sequence are the same as for the original sequence and that the singularity properties are similar. Finally we discuss the Emden-Fowler sequence in terms of its singularity and symmetry properties. / Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2009.

by Alan J. Laub. / Bibliography: p. 44-46. / Research supported by Contract ERDA-E(49-18)-2087.

by T. Pappas, A.J. Laub, N.R. Sandell, Jr. / Bibliography: leaf 38. / "May 1979." / Contract ERDA-E(49-18)-2087 Contract No. DAAG29-79-C-0031

This thesis is intended to be a survey on the comparison theorems and oscillation theorems for second order linear differential equations. We shall discuss four comparison theorems in detail: Sturm-Picone, Levin, Reid and Leighton comparison theorems. For oscillation properties, we shall study Hille-Kneser theorems, and Wintner and Leighton oscillation criteria, which involves analysis of a Riccati equation. In 1969, J.S.W. Wong had some deep results about oscillatory and nonoscillatory differential equations. We shall explain these results and some of the examples in detail. This survey is mainly based on the monographs of Swanson [12], and Deng [20], plus a paper of Wong [18]. In some places, we give simplifications and extensions.

Thesis (M.S.)--Missouri University of Science and Technology, 2008. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed April 14, 2008) Includes bibliographical references (p. 119-121).

Thesis (M.Sc. (Applied Mathematics))--Mahidol University, 1983.

by Norman August Lehtomaki. / Bibliography: p. 161-163. / Originally presented as the author's thesis, (M.S.) in the M.I.T. Dept. of Electrical Engineering and Computer Science, 1978. / Prepared under Dept. of Energy, Division of Electric Energy Systems Grant ERDA-E(49-18)-2087.

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