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 )) = 0 under 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 (H 1 ):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 ( H 1 ) and ( H 2 ): the real valued functions m and n are continuous on a non-trivial interval J of reals.