References
R. J. Ballieu and K. Pfeiffer, Attractivity of the origin for the equationx″+f(t, x, x′)|x′| ax′+g(x)=0,J. Math. Anal. Appl.,65 (1978), 321–332.
T. A. Burton, Uniform asymptotic stability in functional differential equations,Proc. Amer. Math. Soc.,68 (1978), 195–199.
L. Becker, T. A. Burton and S. Zhang, Functional differential equations and Jensen's inequality,J. Math. Anal. Appl.,138 (1989), 137–156.
T. A. Burton, A. Casal and A. Somolinos, Upper and lower bounds for Liapunov functionals,Funkcial. Ekvac.,32 (1989), 23–55.
T. A. Burton and L. Hatvani, Stability theorems for nonautonomous functional differential equations by Liapunov functionals,Tohoku Math. J.,41 (1989), 65–104.
S. N. Busenberg and K. L. Cooke, Stability conditions for linear non-autonomous delay differential equations,Quart. Appl. Math.,42 (1984), 295–306.
N. N. Krasovskii,Stability of Motion, Stanford University Press (1963).
G. Makay, On the asymptotic stability in terms of two measures for functional differential equations,J. Nonlinear Anal.,16 (1991), 721–727.
M. Marachkov, On a theorem on stability,Bull. Soc. Phy. Math., Kazan,12 (1940), 171–174.
R. A. Smith, Asymptotic stability ofx″+a(t)x′+x=0,Quart. J. Math. Oxford Ser. (2),12 (1961), 123–126.
L. H. Thurston and J. S. W. Wong, On global stability of certain second order differential equations with integrable forcing terms,SIAM J. Appl. Math.,24 (1973), 50–61.
T. Wang, Asymptotic stability and the derivatives of solutions of functional differential equations,Rocky Mountain J., to appear.
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Burton, T.A., Makay, G. Asymptotic stability for functional differential equations. Acta Math Hung 65, 243–251 (1994). https://doi.org/10.1007/BF01875152
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DOI: https://doi.org/10.1007/BF01875152