Nonprincipal solutions of half-linear second order differential equations Original Research Article

We consider the nonoscillatory half-linear second order differential equation equation(∗) View the MathML source(r(t)Φ(x′))′+c(t)Φ(x)=0,Φ(x)=|x|p−2x,p>1, Turn MathJax on and we suppose that we know its principal solution View the MathML sourcex̃. We establish an asymptotic formula for nonprincipal solutions of (∗) and we use this asymptotic formula to obtain an oscillation criterion for (∗).