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

Abstract

The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important role in determining the right way to study these equation. An example to illustrate the results is given.

More Effective Results for Testing Oscillation of Non-Canonical Neutral Delay Differential Equations

“…The conditions obtained do not use unknown functions and provide more precise results than those presented in [22]. Moreover, by studying the non-canonical case, our results complement the results in [4][5][6][7]14].…”

“…To the best of our knowledge, the number of works dealing with the study of higherorder neutral differential equations in the non-canonical case is much smaller than those that deal with equations in the canonical case (see [4][5][6][7][8][9][10][11][12][13][14][15][16]). On the other hand, it is easy to find many works that have dealt with non-canonical higher-order equations with delay but not neutral (see for example [17][18][19][20]).…”

Quantum mechanics with spatial non-local effects and position-dependent mass

“…2) is comparable to the Fisher-Kolmogorov equation when M 2 > 0 [80] and to the Swift-Hohenberg equation when M 2 < 0 [81]. Equation (3.2) is also associated with the oscillatory behaviour of 4th-order differential equations discussed largely in dynamical systems [82][83][84][85][86][87]. The sign of M 2 is very significant and influences the quantum motion of the particle and hence, the case where M 4 > 0, provides a stabilized quantum dynamics.…”

Neutral Differential Equations of Higher-Order in Canonical Form: Oscillation Criteria

“…Several researchers have investigated the oscillatory behaviour of even-order DEs under various conditions. For more information, see [12][13][14][15][16][17][18][19][20]. We mention in some detail:…”