On the boundedness and the stability of solutions of some differential equations of the fourth order

Some remarks on the stability and boundedness of solutions of certain differential equations of fourth-order

“…Theorem 2 revises and improves the second result obtained in [35], and generalizes the results of Ezeilo [8], Harrow [11] and Tunç [42, Theorem 2.7].…”

“…In accordance with the representation Then by an argument similar to that in the proof of the theorem in Ezeilo [8], one may show that the inequality in Lemma 4 can be easily obtained. Hence the details of the proof are omitted.…”

On stability and boundedness of solutions of a certain fourth‐order delay differential equation

“…V(x(t), y(t), z(t), w(t)) Define the Lyapunov function V V(x(t), y(t), z(t), w(t)) by Then, by the analysis in [7], V(0,0,0,0) g(y(t)) < ala2 ly(t)l; and f(z(t)) < a2a3/a4. Therefore, dlg'(y(t)) dzf(Z(t)) a 2 (+I/al)g'(y(t)) ( Given any solution (x,y,z,w) of (2.5)…”

“…Essentially, our main aim here is to use the Lyapunov function utilized by Ezeilo in [7] for ordinary differential equations to attempt to prescribe some sufficient conditions that guarantee the uniform asymptotic stability and the boundedness of the solutions of the fourth-order delay differential equation of the form "'t) + f('(t))'(t) + 2"(t) + 82"(t-h) + g( (t-h)) + 4…”

Stability and boundedness results for certain nonlinear vector differential equations of the fourth order

“…In the case n = 1, Theorem 1 includes the first results of Tunç (Theorem 1 in [27]) except that some minor modifications arise in the conditions established here and in Theorem 1 in [24], Ezeilo [9,10], Harrow [12], and Wu and Xiong [38], and it also improves the results of [9,10,12] and [38] except for the restriction…”