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

Abstract

In this paper we consider the equation(1.1) (r(t)y′(t))′+p(t)f(y(t)) = 0under 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)) = 0under the conditions (H1) and(H2): the real valued functions m and n are continuous on a non-trivial interval J of reals.