An Oscillation Criterion of Nonlinear Differential Equations with Advanced Term

Abstract

The aim of the present paper is to provide oscillation conditions for fourth-order damped differential equations with advanced term. By using the Riccati technique, some new oscillation criteria, which ensure that every solution oscillates, are established. In fact, the obtained results extend, unify and correlate many of the existing results in the literature. Furthermore, two examples with specific parameter values are provided to confirm our results.

New Criteria for Oscillation of Half-Linear Differential Equations with p-Laplacian-like Operators

“…Then, there exists a ı 1 ≥ ı 0 such that w(ı) > 0 and w(φ i (ı)) > 0 for ı ≥ ı 1 . From Lemmas 1 and 4, we find that w (ı) > 0, w (ı) < 0 and w (ı) > 0, (17) for ı ≥ ı 2 , where ı 2 is sufficiently large. Now, integrating (1) from ı to l, we have…”

“…Therefore, there are many studies on the oscillation criteria of different orders of some differential equations with p-Laplacianlike operators; see [8,9]. With regard to their practical importance, the oscillation and asymptote of delay differential equations have been studied extensively in recent decades; see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Third-Order Neutral Differential Equations with Damping and Distributed Delay: New Asymptotic Properties of Solutions

“…In recent years, differential equations and their symmetric properties have received much attention, since they have a wide application related to the various phenomena of life. For instance, differential equations appeared in the modeling of population growth, as they were associated with various life sciences such as biology, neural networks and chemical reactions (see [1][2][3] and, for nonlinear dynamic systems [4][5][6]).…”