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Non-oscillation and asymptotic properties for a class of forced second-order nonlinear equations

Published online by Cambridge University Press:  24 October 2008

Lynn H. Erbe ,
V. Sree Hari Rao  and
K. V. V. Seshagiri Rao
Lynn H. Erbe
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
V. Sree Hari Rao
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1 Department of Mathematics, Osmania University, Hyderabad – 500007, India
K. V. V. Seshagiri Rao
Affiliation:
Department of Mathematics, Osmania University, Hyderabad – 500007, India
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Extract

Consider the second order nonlinear equation

where, r, p, f ε C ([a, + ∞), R), R = (–∞, +∞) with r > 0 and λ > 0 is the quotient of odd integers. One of the prototypes of this class of equations is the generalized Thomas-Fermi of Emden-Fowler equation

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 1 , January 1984 , pp. 155 - 163
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1] Bellman, R.. Stability Theory of Differential Equations (McGraw-Hill, 1953).Google Scholar
[2] Hille, E.. Some aspects of the Thomas-Fermi equation. J. Analyse Math. 23 (1970), 147–170.CrossRefGoogle Scholar
[3] Hille, E.. Aspects of Emden's equation. J. Fac. Sci. Univ. Tokyo Sect. I A Math. 17 (1970), 11–30.Google Scholar
[4] Jackson, L. K.. Subfunctions and second order ordinary differential inequalities. Adv. in Math. 2 (1968), 307–363.CrossRefGoogle Scholar
[5] Maric, V. and Skendzic, M.. Unbounded solutions of the generalized Thomas-Fermi equation. Math. Balkanica 3 (1973), 312–320.Google Scholar
[6] Parhi, N. and Nayak, S. K.. On the behaviour of solutions of y″ − p(t)yr = f(t). Applicable Anal. 9 (1979), 1–5.CrossRefGoogle Scholar
[7] Parhi, N. and Nayak, S. K.. On non-oscillatory behaviour of solutions of nonlinear differential equations. Accad. Naz. dei Lincei, Serie VIII, 65 (1978), 58–62.Google Scholar
[8] Taliaferro, S. D.. Asymptotic behavior of solutions of y” = ø (t)y λ. J. Math. Anal. Appl. 66 (1978), 95–134.CrossRefGoogle Scholar
[9] Wong, J. S. W.. On the generalized Emden-Fowler equation. Siam Rev. 17 (1975), 339–360.CrossRefGoogle Scholar
[10] Wong, P. K.. Existence and asymptotic behavior of proper solutions of a class of second order nonlinear differential equations. Pacific J. Math. 13 (1963), 737–760.CrossRefGoogle Scholar
[11] Wong, P. K.. Bounds for solutions to a class of nonlinear second-order differential equations. J. Differential Equations 7 (1970), 139–146.CrossRefGoogle Scholar