Extremal solutions for a class of nonlinear differential equations-Reference-Cited by-同舟云学术

Extremal solutions for a class of nonlinear differential equations

Published:1980 Issue:3 Volume:79 Page:415-421
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Kreith Kurt

Abstract

Positive solutions of y ( n ) ± f ( t , y ) = 0 {y^{(n)}} \pm f(t,y) = 0 are characterized as maximal or minimal depending on whether their asymptotic behavior is O ( t n − 1 ) O({t^{n - 1}}) or O ( 1 ) O(1) , respectively. Necessary and sufficient conditions for the existence of such extremal solutions are established.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1980-079-03/S0002-9939-1980-0567983-8/S0002-9939-1980-0567983-8.pdf

Reference6 articles.

1. On monotone solutions of systems of non-linear differential equations;Hartman, Philip;Amer. J. Math.,1954

2. Nonlinear differential equations with monotone solutions;Kreith, Kurt;Pacific J. Math.,1979

3. Nonlinear oscillation of fourth order differential equations;Kusano, Takaŝi;Canadian J. Math.,1976

4. Some questions of the theory of almost periodic functions. I;Levitan, B. M.;Uspehi Matem. Nauk (N.S.),1947

5. Oscillatory property of ordinary differential equations of arbitrary order;Onose, Hiroshi;J. Differential Equations,1970

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