On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation

Abstract EN

This paper presents two methods to obtain upper bounds for the distance between a zero and an adjacent critical point of a solution of the second-order half-linear differential equation (p(x)Φ(y'))'+q(x)Φ(y)=0, with p(x) and q(x) piecewise continuous and p(x)>0, Φ(t)=|t|r-2t and r being real such that r>1.

It also compares between them in several examples.

Lower bounds (i.e., Lyapunov inequalities) for such a distance are also provided and compared with other methods.