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Monotone solutions of a class of second order nonlinear differential equations. (English) Zbl 0552.34053

The asymptotic behavior of the solutions of \([p(t)F(x(t))x'(t)]'=q(t)g(x(t))\) is studied. Some necessary and sufficient conditions for boundedness of the solutions and an asymptotic comparison theorem are established. Oscillatory solutions are excluded by the hypotheses. The proofs are constructive.
Reviewer: W.Ames

MSC:

34E05 Asymptotic expansions of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34C11 Growth and boundedness of solutions to ordinary differential equations
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[1] Fleishman, B. A.; Mahar, T. J., A step function model in chemical reactor theory: multiplicity and stability of solutions, Nonlinear Analysis, 5, 645-654 (1981) · Zbl 0461.34015
[2] Komkov, V., Continuability and estimates of solutions of \((a(t)φ(x)x\)′)′ + \(c(t)f(x) = 0\), Ann. Polon. Math., XXX, 125-137 (1974) · Zbl 0251.34003
[3] Mahfoud, W. E.; Rankin, S. M., Some properties of solutions of \((r( tψ (x)x\)′)′ + \(a(t)f(x) = 0\), SIAM J. math. Analysis, 10, 49-54 (1979) · Zbl 0397.34004
[4] Marini, M.; Zezza, P., On the asymptotic behaviour of the solutions of a class of second order linear differential equations, J. diff. Eqns., 28, 1-17 (1978) · Zbl 0371.34032
[5] Marivi, M.; Zezza, P., Sul carattere oscillatorio della soluzioni di equazioni differenziali non lineari del secondo ordine, Bull. Un. mat. Ital., 5, 1110-1123 (1980) · Zbl 0442.34032
[6] Oddson, J. K.; Metcalf, F. T., An asymptotic comparison theorem, Le Matematiche, 33, 306-320 (1978) · Zbl 0488.34024
[7] Spansone, G., Equazioni Differenziali in Campo Reale, Vol. II (1948), Zanichelli: Zanichelli Bologna
[8] Swanson, C. A., Comparison and Oscillatory Theory of Linear Differential Equations (1968), Academic Press: Academic Press New York · Zbl 0191.09904
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