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LINEAR ASYMPTOTIC BEHAVIOUR OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Published online by Cambridge University Press:  01 January 2007

MATS EHRNSTRÖM
MATS EHRNSTRÖM*
Affiliation:
Centre for Mathematical Sciences, Lund University, PO Box 118, 22100 Lund, Sweden. e-mail: mats.ehrnstrom@math.lu.se
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Abstract.

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We study the semilinear differential equation u″ + F(t,u,u′)=0 on a half-line. Under different growth conditions on the function F, equations with globally defined solutions asymptotic to lines are characterized. Both fixed initial data and fixed asymptote are considered.

Keywords

34A1234E10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 1 , January 2007 , pp. 105 - 120
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

REFERENCES

1.Atkinson, F. V., On second order nonlinear oscillation, Pacific J. Math. 5 (1955), 643–647.CrossRefGoogle Scholar
2.Bielecki, A., Une remarque sur la méthode de Banach-Cacciopoli-Tikhonov dans la théorie des équations differéntielles ordinaires, Bull. Acad. Polon. Sci. 4 (1956), 261–264.Google Scholar
3.Constantin, A., Global existence of solutions for perturbed differential equations, Ann. Mat. Pura Appl. 168 (1995), 237–299.CrossRefGoogle Scholar
4.Constantin, A., On the existence of positive solutions of second order differential equations, Ann. Mat. Pura Appl. 184 (2005), 131–138.CrossRefGoogle Scholar
5.Dubé, S. G., and Mingarelli, A. B., Note on a non-oscillation theorem or Atkinson, Electron. J. Differential Equations 22 (2004), 1–6.Google Scholar
6.Ehrnström, M., Positive solutions for second-order nonlinear differential equations, Nonlinear Anal. 64 (2006), 1608–1620.CrossRefGoogle Scholar
7.Ehrnström, M., Prescribed asymptotic behaviour of solutions to semilinear ordinary differential equations, Appl. Math. Lett., to appear.Google Scholar
8.Ehrnström, M. and Mustafa, O. G., On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal., to appear.Google Scholar
9.Hallam, T., Asymptotic integration of second order differential equation with integrable coefficients, SIAM J. Appl. Math. 19 (1970), 430–439.CrossRefGoogle Scholar
10.Kusano, T. and Naito, M., Unbounded nonoscillatory solutions of nonlinear ordinary differential equations of arbitrary order, Hiroshima Math. J. 18 (1988), 361–372.CrossRefGoogle Scholar
11.Kusano, T., Naito, M. and Usami, H., Asymptotic behavior of solutions of a class of second order nonlinear differential equations, Hiroshima Math. J. 16 (1986), 149–159.CrossRefGoogle Scholar
12.Lipovan, O., On the asymptotic behaviour of the solutions to a class of second order nonlinear differential equations, Glasgow Math. J. 45 (2003), 179–187.CrossRefGoogle Scholar
13.Mustafa, O. G., Initial value problem with infinitely many linear-like solutions for a second-order differential equation, Appl. Math. Lett. 18 (2005), 931–934.CrossRefGoogle Scholar
14.Mustafa, O. G. and Rogovchenko, Y. V., Global existence of solutions with prescribed asymptotic behavior for second-order nonlinear differential equations, Nonlinear Anal. 51 (2002), 339–368.CrossRefGoogle Scholar
15.Mustafa, O. G. and Rogovchenko, Y. V., Asymptotic integration of nonlinear differential equations, Nonlinear Anal. 63 (2005), 2135–2143.CrossRefGoogle Scholar
16.Philos, Ch., Purnaras, I., and Tsamatos, P., Asymptotic to polynomials solutions for nonlinear differential equations, Nonlinear Anal. 59 (2004), 1157–1179.CrossRefGoogle Scholar
17.Usami, H., Global existence and asymptotic behavior of solutions of second-order nonlinear differential equations, J. Math. Anal. Appl. 122 (1987), 152–171.CrossRefGoogle Scholar
18.Wahlén, E., Positive solutions of second-order differential equations, Nonlinear Anal. 58 (2004), 359–366.CrossRefGoogle Scholar
19.Yin, Z., Monotone positive solutions of second-order nonlinear differential equations, Nonlinear Anal. 54 (2003), 391–403.CrossRefGoogle Scholar
20.Zeidler, E., Nonlinear functional analysis and its applications I: fixed-point theorems (Springer-Verlag, 1985).CrossRefGoogle Scholar