Behavior of Solutions of Second-Order Differential Equations with Sublinear Damping

J. Karsai, J. R. Graef, and C. Qian, “Asymptotic behavior of solutions of oscillator equations with sublinear damping,” Commun. Appl. Anal., 6, 49–59 (2002).

J. Karsai, J. R. Graef, and C. Qian, “Nonlinear damping in oscillator equations,” in: Proc. Conf. Different. and Difference Equat. “CDDE 2002,” Folia FSN Univ. Masarykianae Brunensis, Mathematica, Vol. 13 (2003), pp. 145–154.

J. Karsai, “On the global asymptotic stability of the zero solution of x″ + g(t, x, x′)x′ + f(x) = 0,” Stud. Sci. Math. Hung., 19, 385–393 (1984).

R. A. Smith, “Asymptotic stability of x″ + a(t)x′ + x = 0,” Quart. J. Math. Oxford, 12, No.2, 123–126 (1961).

L. Hatvani, “On the stability of the zero solution of certain second order differential equations,” Acta Sci. Math., 32, 1–9 (1971).

J. Karsai and J. R. Graef, Attractivity Properties of Oscillator Equations with Superlinear Damping (to appear).

R. J. Ballieu and K. Peiffer, “Attractivity of the origin for the equation $$\ddot x + f(t,x,\dot x)|\dot x|^\varphi \dot x + g(x) = 0$$ ,” J. Math. Anal. Appl., 65, 321–332 (1978).

L. Hatvani, “Nonlinear oscillation with large damping,” Dynam. Syst. Appl., 1, 257–270 (1992).

L. Hatvani, T. Krisztin, and V. Totik, “A necessary and sufficient condition for the asymptotic stability of the damped oscillator,” J. Different. Equat., 119, 209–223 (1995).

L. Hatvani and V. Totik, “Asymptotic stability of the equilibrium of the damped oscillator,” Different. Integr. Equat., 6, 835–848 (1993).

J. Karsai, “On the asymptotic stability of the zero solution of certain nonlinear second order differential equations,” Different. Equat.: Qual. Theory, Colloq. Math. Soc. J. Bolyai, 47, 495–503 (1987).