An Improved Criterion for the Oscillation of Fourth-Order Differential Equations

Abstract

The main purpose of this manuscript is to show asymptotic properties of a class of differential equations with variable coefficients r ν w ‴ ν β ′ + ∑ i = 1 j q i ν y κ g i ν = 0 , where ν ≥ ν 0 and w ν : = y ν + p ν y σ ν . By using integral averaging technique, we get conditions to ensure oscillation of solutions of this equation. The obtained results improve and generalize the earlier ones; finally an example is given to illustrate the criteria.

Some New Oscillation Results for Fourth-Order Neutral Differential Equations with Delay Argument

“…In the last few decades, there has been a constant interest to investigate the asymptotic property for oscillations of differential equations [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and nonlinear neutral differential equations, see [20][21][22][23][24][25][26][27][28][29][30][31][32]. Oscillation of nonlinear differential equations with delay arguments has been further developed in recent years.…”

New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

“…(a) Assume that f (λ) > 0 for λ ≥ λ 2 . We easily get (15). Then, proceeding as in Case 1 in the proof of Theorem 3, we get a contradiction.…”

Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms

“…In particular, it is a necessary and invaluable issue, either theoretically or practically, to probe into neutral differential equations with distributed deviating arguments. Hence, a scientific study of the qualitative properties of solutions of these equations is proposed for applications, see for example the book [7,8] and the papers [9][10][11][12][13][14][15].…”