Fite and Kamenev type oscillation criteria for second order elliptic equations

Abstract

Abstract. Fite and Kamenev type oscillation criteria for the second order nonlinear damped elliptic differential equationare obtained. Our results are extensions of those for ordinary differential equations and improve some known oscillation criteria in the literature. Several examples are given to show the significance of the results.

Annual oscillation criteria for second-order nonlinear elliptic differential equations

“…(2) up to 1979. For recent contributions, we refer the reader to [12,13] in which a classical Kamenev theorem [4] is to be extended to Eq. (2).…”

Oscillation Theorems for Nonlinear Second Order Elliptic Equations

“…Other related results on the oscillation for (1.2) and (1.3) can also been found in recent papers [9,10,13,[16][17][18][19][20][21][22].…”

Oscillation of second-order elliptic equations with damping terms

“…Without this term, our method cannot be applied to damped elliptic equation (1.1) (cf. [9,[11][12][13][14][15][16][17]). …”

“…Recently, this technique was explored further by Xu [12] and Zhang et al [17], who established Kamenev-type oscillation criteria [7] for (E 2 ), respectively. For (E 2 ), as more late work in this direction we refer the reader to the papers [13][14][15][16] and references cited therein. In this paper we will study oscillation of the second-order elliptic differential equation with damping terms…”