Bargmann-type inequality for half-linear differential operators (Q962405)

By means of the Riccati technique, the authors obtain a Bargmann-type necessary condition for the existence of a nontrivial solution of the following perturbed half-linear Euler differential equation with at least \((n+1)\) zero points in \((0,\infty )\): \[ (\Phi(x^{\prime}))^{\prime}+[\gamma/t^{p}+c(t)]\Phi(x)=0, \] where \(\Phi (x):=|x|^{p - 2}x, p>1\), with the subcritical coefficient \(\gamma <\gamma _{p}:=((p - 1)/p)^p\). The presented Bargmann-type inequality for half-linear differential operators includes that for linear the case (\(p=2\)) as special one and will be helpful to further understand the half-linear oscillation theory.