Liapunov-type inequality for higher order differential equations

Year, pages: 2002, 31 - 46

In this paper, Liapunov-type inequalities are obtained for higher order nonlinear, nonhomogeneous differential equations. These inequalities are used to obtain criteria for disconjugacy of linear homogeneous equations on an interval and to show that oscillatory solutions of the equation converge to zero as $ t \to ∞$. It is also shown, using these inequalities, that $(t_m+k - t_m) \to ∞$ as $ m \to ∞$, where $ 1≤ k≤ n-1$ and $\{t_m\}$ is an increasing sequence of zeros of an oscillatory solution of $Dⁿ y+p(t)y =0$, $t≥ 0$, provided that $p \in L^σ([0, ∞), \Bbb R)$, $1 ≤ σ < ∞$.

Parhi, N., Panigrahi, S. 2002. Liapunov-type inequality for higher order differential equations. In Mathematica Slovaca, vol. 52, no.1, pp. 31-46. 0139-9918.

Parhi, N., Panigrahi, S. (2002). Liapunov-type inequality for higher order differential equations. Mathematica Slovaca, 52(1), 31-46. 0139-9918.