A comparison theorem and oscillation criteria for second-order nonlinear differential equations

This paper presents a new comparison theorem for the oscillation of solutions of second-order nonlinear differential equations of the form (ϕp(x′))′+1tpf(x)=0, where p>1p>1 and ϕp(x)=|x|p−2xϕp(x)=|x|p−2x and f(x)f(x) satisfies the signum condition xf(x)>0xf(x)>0 if x≠0x≠0, but is not assumed to be monotone. Combining the comparison theorem and known oscillation criteria, we can also derive new oscillation criteria for the equations. Proof is established by means of phase plane analysis of systems.