Qualitative Behavior of Solutions of Second Order Differential Equations

Abstract

In this work, we study the oscillation of second-order delay differential equations, by employing a refinement of the generalized Riccati substitution. We establish a new oscillation criterion. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. We illustrate the results with some examples.

Improved Conditions for Oscillation of Functional Nonlinear Differential Equations

“…The criterion c 0 > 60 c 0 > 28. 7 From above, we see that [10] improved the results in [9]. The motivation in studying this paper is complementary and improves the results in [9,10].…”

“…More and more scholars pay attention to the oscillatory solution of functional differential equations, see [2][3][4][5], especially for the second/third-order, see [6][7][8], or higher-order equations see [9][10][11][12][13][14][15][16][17]. With the development of the oscillation for the second-order equations, researchers began to study the oscillation for the fourth-order equations, see [18][19][20][21][22][23][24][25].…”

A Philos-Type Oscillation Criteria for Fourth-Order Neutral Differential Equations

“…From Lemma 6, we get that (9) holds. Multiplying (9) by H 2 (t, s) and integrating the resulting inequality from t 1 to t, we obtain t t 1…”

The Oscillatory of Linear Conformable Fractional Differential Equations of Kamenev Type

“…Because it combines the best properties, many research studies have increased their research on it in recent years. Although there is much about the oscillations of fractional differential equations (see [15][16][17][18][19][20][21][22][23][24][25][26][27][28] and the references therein), there is little about the conformable fractional differential equations of Kamenev type.…”