Forced oscillations of half-linear elliptic equations via Picone-type inequality.

Yoshida, Norio

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This paper is concerned with a class of even order nonlinear differential equations of the form $\frac{d}{d t} (| {(x (t) + p (t) x (τ (t)))}^{(n - 1)} |^{α - 1} {(x (t) + p (t) x (τ (t)))}^{(n - 1)}) + F (t, x (g (t))) = 0,$ where $n$ is even and $t \geq t_{0}$ . By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of existing results. Our results are more general and sharper than some previous results even for second order equations.