Lyapunov type inequalities for second-order half-linear differential equations (Q549814)

Some new Lyapunov inequalities are established for the second-order half-linear differential equations of the type \[ ( r(t) |x'(t)|^{\gamma -2} x'(t) )' + q(t) |x(t)|^{\gamma -2}x(t) = 0 \] and \[ ( |x'(t)|^{\gamma -2} x'(t) )'+ p(t)|x'(t)|^{\gamma -2}x'(t)+ q(t) |x(t)|^{\gamma -2}x(t) = 0\,. \] The inequalities generalize and extend results cited from the literature.