Geodesic
Lyapunov Inequalities and Bounds on Solutions of Certain Second Order Equations*
Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 499-504

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In this paper we consider the equation(1.1) (r(t)y′(t))′+p(t)f(y(t)) = 0under the conditions((H 0): 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)) = 0under the conditions (H 1) and(H 2): the real valued functions m and n are continuous on a non-trivial interval J of reals. 
Eliason, Stanley B. Lyapunov Inequalities and Bounds on Solutions of Certain Second Order Equations*. Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 499-504. doi: 10.4153/CMB-1974-088-2
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