On the number of zeros of nonoscillatory solutions to second-order half-linear differential equations (Q2714174)

The authors consider the second-order half-linear differential equation NEWLINE\[NEWLINE({y'}^{\alpha*})'=\lambda q(t)y^{\alpha*}=0NEWLINE\]NEWLINE defined on a half-line, where \(u^{\alpha*}\) denotes the function \(|u|^{\alpha}\text{sgn} u\). They make the following hypotheses: \(\alpha, \lambda>0\) are given constants, and \(q\) is a piecewise continuous, nonnegative function, defined on a half-line, which is nonidentically zero on any sub-half-line of its domain. The results concern the number of zeros of nonoscillatory solutions to such equations. In the first section of the paper, the authors present preliminary results and motivation for this problem.