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Lyapunov Inequalities and Bounds on Solutions of Certain Second Order Equations*

Published online by Cambridge University Press:  20 November 2018

Stanley B. Eliason
Stanley B. Eliason*
Affiliation:
University of Oklahoma, Norman, Oklahoma 73069
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In this paper we consider the equation

(1.1) (r(t)y′(t))′+p(t)f(y(t)) = 0

under the conditions

((H0): the real valued functions r, r′ and p are continuous on a non-trivial interval J of reals, and r(t)>0 for t∈J;

and

(H1):f:R→R is continuously differentiable and odd with f'(y)>0 for all real y. We also consider the equation

(1.2) y″(t)+m(t)y′(t)+n(t)f(y(t)) = 0

under the conditions (H1) and

(H2): the real valued functions m and n are continuous on a non-trivial interval J of reals.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 499 - 504
Copyright
Copyright © Canadian Mathematical Society 1974

Footnotes

*

Based on research supported in part by the U.S. Army Research Office-Durham through Grant Number DA-ARO-D-31-124-72-G154 with the University of Oklahoma Research Institute.

References

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