Explicit bounds for the solutions of second order linear differential equations

This paper deals with the construction of explicit bounds for solutions of second order linear differential equations of the type [p(x)y′(x)]′+q(x)y(x)=0[p(x)y′(x)]′+q(x)y(x)=0, p(x),q(x)>0p(x),q(x)>0, x>x0x>x0. The construction is based on the study of the evolution of two complementary functionals involving y(x)y(x) in the sequence of zeroes of y(x)y(x) and y′(x)y′(x). Based on that, both a theoretical bound and an algorithm to explicitly calculate that bound are presented. An illustrative example shows that the bounds proposed here improve previous results.