On the oscillatory integration of some ordinary differential equations
Mustafa, Octavian G.
Archivum Mathematicum, Tome 044 (2008), p. 23-36 / Harvested from Czech Digital Mathematics Library
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Conditions are given for a class of nonlinear ordinary differential equations $x^{\prime \prime }+a(t)w(x)=0$, $t\ge t_0\ge 1$, which includes the linear equation to possess solutions $x(t)$ with prescribed oblique asymptote that have an oscillatory pseudo-wronskian $x^{\prime }(t)-\frac{x(t)}{t}$.

Publié le : 2008-01-01
Classification:  34C10,  34D05,  34E05,  34K25 
@article{108093,
     author = {Octavian G. Mustafa},
     title = {On the oscillatory integration of~some~ordinary differential~equations},
     journal = {Archivum Mathematicum},
     volume = {044},
     year = {2008},
     pages = {23-36},
     zbl = {1212.34145},
     mrnumber = {2431228},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108093}
}

Mustafa, Octavian G. On the oscillatory integration of some ordinary differential equations. Archivum Mathematicum, Tome 044 (2008) pp. 23-36. http://gdmltest.u-ga.fr/item/108093/

Agarwal, R. P.; Djebali, S.; Moussaoui, T.; Mustafa, O. G. On the asymptotic integration of nonlinear differential equations, J. Comput. Appl. Math. 202 (2007), 352–376. (2007) | Article | MR 2319962 | Zbl 1123.34038

Agarwal, R. P.; Djebali, S.; Moussaoui, T.; Mustafa, O. G.; Rogovchenko, Yu. V. On the asymptotic behavior of solutions to nonlinear ordinary differential equations, Asymptot. Anal. 54 (2007), 1–50. (2007) | MR 2356463

Agarwal, R. P.; Mustafa, O. G. A Riccatian approach to the decay of solutions of certain semi-linear PDE’s, Appl. Math. Lett. 20 (2007), 1206–1210. (2007) | Article | MR 2384247 | Zbl 1137.35356

Atkinson, F. V. On second order nonlinear oscillation, Pacific J. Math. 5 (1995), 643–647. (1995) | Article | MR 0072316

Bartušek, M.; Došlá, Z.; Graef, J. R. The nonlinear limit-point/limit-circle problem, limit-circle problem, Birkhäuser, Boston, 2004. (2004) | MR 2020682 | Zbl 1052.34021

Cecchi, M.; Marini, M.; Villari, G. Integral criteria for a classification of solutions of linear differential equations, J. Differential Equations 99 (1992), 381–397. (1992) | Article | MR 1184060 | Zbl 0761.34009

Cecchi, M.; Marini, M.; Villari, G. Comparison results for oscillation of nonlinear differential equations, NoDEA Nonlinear Differential Equations Appl. 6 (1999), 173–190. (1999) | Article | MR 1694795 | Zbl 0927.34023

Constantin, A. Existence of positive solutions of quasilinear elliptic equations, Bull. Austral. Math. Soc. 54 (1996), 147–154. (1996) | Article | MR 1402999 | Zbl 0878.35040

Constantin, A. Positive solutions of quasilinear elliptic equations, J. Math. Anal. Appl. 213 (1997), 334–339. (1997) | Article | MR 1469378 | Zbl 0891.35033

Deng, J. Bounded positive solutions of semilinear elliptic equations, J. Math. Anal. Appl. 336 (2007), 1395–1405. (2007) | Article | MR 2353022 | Zbl 1152.35367

Djebali, S.; Moussaoui, T.; Mustafa, O. G. Positive evanescent solutions of nonlinear elliptic equations, J. Math. Anal. Appl. 333 (2007), 863–870. (2007) | Article | MR 2331699 | Zbl 1155.35029

Dugundji, J.; Granas, A. Fixed point theory I, Polish Sci. Publ., Warszawa, 1982. (1982) | MR 0660439

Ehrnström, M. Positive solutions for second-order nonlinear differential equations, Nonlinear Anal. 64 (2006), 1608–1620. (2006) | Article | MR 2200162 | Zbl 1101.34022

Ehrnström, M.; Mustafa, O. G. On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal. 67 (2007), 1147–1154. (2007) | Article | MR 2325368 | Zbl 1165.35016

Gilbarg, D.; Trudinger, N. S. Elliptic partial differential equations of second order, Springer-Verlag, Berlin, 2001. (2001) | MR 1814364 | Zbl 1042.35002

Hartman, P. On non-oscillatory linear differential equations of second order, Amer. J. Math. 74 (1952), 389–400. (1952) | Article | MR 0048667 | Zbl 0048.06602

Heidel, J. W. A nonoscillation theorem for a nonlinear second order differential equation, Proc. Amer. Math. Soc. 22 (1969), 485–488. (1969) | Article | MR 0248396 | Zbl 0169.42203

Hesaaraki, M.; Moradifam, A. On the existence of bounded positive solutions of Schrödinger equations in two-dimensional exterior domains, Appl. Math. Lett. 20 (2007), 1227–1231. (2007) | Article | MR 2384252 | Zbl 1137.35429

Kiguradze, I. T.; Chanturia, T. A. Asymptotic properties of solutions of nonautonomous ordinary differential equations, Kluwer, Dordrecht, 1993. (1993) | Zbl 0782.34002

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. (2005) | Article | MR 2152306 | Zbl 1095.34505

Mustafa, O. G. On the existence of solutions with prescribed asymptotic behaviour for perturbed nonlinear differential equations of second order, Glasgow Math. J. 47 (2005), 177–185. (2005) | Article | MR 2200965 | Zbl 1072.34049

Mustafa, O. G.; Rogovchenko, Yu. V. Global existence and asymptotic behavior of solutions of nonlinear differential equations, Funkcial. Ekvac. 47 (2004), 167–186. (2004) | Article | MR 2108671 | Zbl 1118.34046

Mustafa, O. G.; Rogovchenko, Yu. V. Limit-point type solutions of nonlinear differential equations, J. Math. Anal. Appl. 294 (2004), 548–559. (2004) | Article | MR 2061342 | Zbl 1057.34023

Mustafa, O. G.; Rogovchenko, Yu. V. Asymptotic integration of a class of nonlinear differential equations, Appl. Math. Lett. 19 (2006), 849–853. (2006) | Article | MR 2240473 | Zbl 1126.34339