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Asymptotic integration of a class of nonlinear differential equations. (English) Zbl 1126.34339
The authors use the well-known Schauder-Tikhonov fixed point theorem to establish existence of solutions with different asymptotic representations at infinity for a class of second order nonlinear differential equations.

MSC:
34D05 Asymptotic properties of solutions to ordinary differential equations
34C41 Equivalence and asymptotic equivalence of ordinary differential equations
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References:
[1] Wong, J.S.W., On second order nonlinear oscillation, Funkcial. ekvac., 11, 207-234, (1968) · Zbl 0157.14802
[2] Constantin, A., On the asymptotic behavior of second order nonlinear differential equations, Rend. mat. appl., 13, 7, 627-634, (1993) · Zbl 0808.34050
[3] Kusano, T.; Trench, W.F., Existence of global solutions with prescribed asymptotic behavior for nonlinear ordinary differential equations, Ann. mat. pura appl., 142, 381-392, (1985) · Zbl 0593.34039
[4] Lipovan, O., On the asymptotic behavior of the solutions to a class of second order nonlinear differential equations, Glasg. math. J., 45, 179-187, (2003) · Zbl 1037.34041
[5] Mustafa, O.G., On the existence of solutions with prescribed asymptotic behavior for perturbed nonlinear differential equations of second order, Glasg. math. J., 47, 177-185, (2005) · Zbl 1072.34049
[6] Mustafa, O.G.; Rogovchenko, Yu.V., Global existence of solutions with prescribed asymptotic behavior for second-order nonlinear differential equations, Nonlinear anal., 51, 339-368, (2002) · Zbl 1017.34005
[7] Mustafa, O.G.; Rogovchenko, Yu.V., Global existence and asymptotic behavior of solutions of nonlinear differential equations, Funkcial. ekvac., 47, 167-186, (2004) · Zbl 1118.34046
[8] Philos, Ch.G.; Purnaras, I.K.; Tsamatos, P.Ch., Asymptotic to polynomials solutions for nonlinear differential equations, Nonlinear anal., 59, 1157-1179, (2004) · Zbl 1094.34032
[9] Rogovchenko, S.P.; Rogovchenko, Yu.V., Asymptotic behavior of certain second order nonlinear differential equations, Dynam. systems appl., 10, 185-200, (2001) · Zbl 0997.34037
[10] Tong, J., The asymptotic behavior of a class of nonlinear differential equations of second order, Proc. amer. math. soc., 84, 235-236, (1982) · Zbl 0491.34036
[11] Masmoudi, S.; Yazidi, N., On the existence of positive solutions of a singular nonlinear differential equation, J. math. anal. appl., 268, 53-66, (2002) · Zbl 1007.34079
[12] Yan, B., Multiple unbounded solutions of boundary value problems for second-order differential equations on the half-line, Nonlinear anal., 51, 1031-1044, (2002) · Zbl 1021.34021
[13] Yin, Z., Monotone positive solutions of second-order nonlinear differential equations, Nonlinear anal., 54, 391-403, (2003) · Zbl 1034.34045
[14] Zhao, Z., Positive solutions of nonlinear second order ordinary differential equations, Proc. amer. math. soc., 121, 465-469, (1994) · Zbl 0802.34026
[15] Constantin, A., Positive solutions of Schrödinger equations in two-dimensional exterior domains, Monatsh. math., 123, 121-126, (1997) · Zbl 0866.35031
[16] Constantin, A.; Villari, G., Positive solutions of quasilinear elliptic equations in two-dimensional exterior domains, Nonlinear anal., 42, 243-250, (2000) · Zbl 0974.35033
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