Stability and boundedness of nonautonomous neutral differential equation with delay
Mathematica Moravica, Tome 24 (2020) no. 1.

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We consider the nonautonomous neutral differential equation with delay \begin{gather*} [ p(t)\Big(q(t)\big(x(t)+\beta_{1} x(t-r_{1})\big)'\Big)'\right] ^{ rime }+a(t)\big(x^{rime rime}(t)+\beta_{2} x''(t-r_{2})\big) +b(t)\big(x^{rime }(t)+\beta_{3} x'(t-r_{3})\big)+c(t)f(x(t-igma))=e(t, x, x', x''). \end{gather*} Using the method of Lyapunov, we give conditions for the uniform asymptotic stability and uniform boundedness and square integrability of solutions for the considered system. Our theorems generalize and extend some related results known in the literature. Example is given to show our results.
Mots-clés : Uniform ultimate boundedness, square integrability, Lyapunov functional, neutral differential equation of third order. 
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Moussadek Remili; Linda D. Oudjedi. Stability and boundedness of nonautonomous neutral differential equation with delay. Mathematica Moravica, Tome 24 (2020) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2020_24_1_a0/