OSCILLATION CRITERIA FOR CERTAIN DAMPED PDE'S WITH p-LAPLACIAN

Abstract

Abstract. Some oscillation criteria are obtained for the damped PDE with pLaplacianThe results established here are extensions of some classical oscillation theorems due to Fite-Wintner and Kamenev for second order ordinary differential equations, and improve and complement recent results of Mařík and Usami.

New Kamenev-type oscillation criteria for half-linear partial differential equations

“…We can easily see that Theorems 3.1-3.8 and other results in [5,6,7,14,15] involve the integral of the functions a ij (x), b i (x), c(x), and hence, require the information of the functions in the whole Ω(r 0 ). By using the techniques in [11,13,17], we can also establish some annulus oscillation criteria for Eq.…”

“…Recently, by using partial Riccati technique [8] , Mařík [5−7] and Xu [14,15] have studied the oscillation of Eq.(1.1). Here our investigation is inspired by [11] in which a new approach based on a class of new functions Φ(r, s, l) [cf, Proposition 1.1] has been developed and is different from the classical Kamenev theorem [3] including extended and improved by Kong [4] , Philos [9] , Rogovchenko and Tuncay [10] , Wong [12] and Yan [16] .…”

On the oscillation of forced second order mixed-nonlinear elliptic equations

“…We refer the reader to papers [5,6,7,10,11,23,24,27,28,32], to monographs [12], [29], and to the references cited there. To the author's knowledge, very little is known about the oscillation of elliptic differential equations with forced terms.…”