Oscillation Criteria for Second Order Half-linear Differential Equations with Damping Term

By using averaging functions, several new oscillation criteria are established for the half-linear damped differential equation-2-2-2-2 r(t) (x) +p(t) |x| x,r(t) (x) +q(t)|x| x=0, dx dx dx dx dt dt dt dt α α α α ψ ϕ ψ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ and the more general equation-2-2 r(t) (x) +p(t) g(x),r(t) (x) +q(t)g(x)=0, d dx dx dx dx dt dt dt dt dt α α ψ ϕ ψ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ where p,q ,r:[t 0 ,∞)→R and ψ,g: R→R are continuous, r(t)>0, p(t)≥0 and ψ(x)>0, xg(x)>0 for x≠0, α>1 a fixed real number. Our results generalize and extend some known oscillation criteria in the literature.