Abstract/Details

ASYMPTOTIC BEHAVIOUR OF NTH ORDER DIFFERENTIAL EQUATIONS WITH MIDDLE TERMS AND FORCINGS

KOSMALA, WITOLD A. J. 
 University of South Florida ProQuest Dissertations Publishing,  1980. 8028937.

Abstract (summary)

Equations of the following types are studied:

(1) x('(n)) + P(t)x('(n-1)) + H(t,x) = Q(t), n (GREATERTHEQ) 4, even,

(2) x('(n)) + P(t)x('(n-2)) + H(t,x) = Q(t), n (GREATERTHEQ) 4, even,

(3) {p(t)x('(n-k))}('(k)) + H(t,x) = Q(t), n, k even, 2 (LESSTHEQ) k (LESSTHEQ) n - 2,

(4) x('(n)) + p(t)x('(n-1)) + q(t)x('(n-2)) + H(t,x) = 0, n (GREATERTHEQ) 4, even or odd.

Several results are obtained concerning the oscillation and other asymptotic properties of the solutions of such equations. The methods involved include the recently developed comparison method of Kartsatos as well as the method of functionals that has been used for third order equations by Lazer, Erbe, and for nth order equations by Kartsatos.

The results obtained utilizing these nonlinear functionals are actually weaker than the corresponding results for third order equations. This is due to the fact that certain terms in the analysis of an nth order equation, containing derivatives of order n - 3, do not enter the corresponding research of third order equations.

Numerous results of Erbe, Foster and Grimmer, Kartsatos, and Kartsatos and Toro are extended to equations of the above types. These results are actually dealing with unforced equations of order 3 and Type (4) (Erbe) or with nth order equations without middle terms and/or forcings.

Since very little research has been done concerning such nonlinear functionals, this work actually constitutes a first attempt towards a general theory of oscillation of equations with middle terms via the study of such functionals. It should also be mentioned that several results in this dissertation are new even in the linear case (H(t,x) (TBOND) r(t)x).

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
ASYMPTOTIC BEHAVIOUR OF NTH ORDER DIFFERENTIAL EQUATIONS WITH MIDDLE TERMS AND FORCINGS
Author
KOSMALA, WITOLD A. J.
Number of pages
122
Degree date
1980
School code
0206
Source
DAI-B 41/06, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9798662116993
University/institution
University of South Florida
University location
United States -- Florida
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
8028937
ProQuest document ID
303100446
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303100446