Kneser solutions of fourth-order trinomial delay differential equations

Oscillation theorems for fourth‐order delay differential equations with a negative middle term

“…Some attempts in this direction have been made by Hou and Cheng 18 and Liang 19 who studied asymptotic and oscillatory properties of the equation y (4) (t) + p(t)y ′ (t) + q(t)y( (t)) = 0 and established criteria for all nonoscillatory solutions to tend to zero near infinity. These results have been recently extended and generalized by present authors, see Džurina et al [20][21][22] The present paper is a continuation of the above-mentioned recent works [18][19][20][21][22] in case when the middle term is negative. As far as we know, there do not appear to be any oscillation results for such equations.…”

“…Following ideas developed in Džurina et al, 21 our technique consists in transforming (E) into its equivalent binomial form which essentially uses positive solutions of an auxiliary third order and its associated second-order differential equation. This allows us to recognize the structure of possible nonoscillatory solutions and to formulate immediately sufficient conditions for oscillation of (E), considering it in binomial form.…”

On oscillation of higher-order advanced trinomial differential equations

“…Example 1 Based on Example 3.5 in [11], we investigate the following linear fourth-order trinomial ADE:…”

“…are oscillatory. In 2015 and 2017, Baculíková, Džurina and Jadlovská [11,13] discussed the oscillatory behaviors of solutions of the two equations…”

Solution of a Class of High Order Differential Equations

“…Some mathematicians investigated existence of solutions for differential equations in [1][2][3][4][5][6]. Some mathematicians studied the solutions of high order differential equations and the theory on differential equations in [7][8][9][10][11].…”