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half-linear ordinary differential equation; asymptotic form
Asymptotic forms of solutions of half-linear ordinary differential equation $\big (|u^{\prime }|^{\alpha -1}u^{\prime }\big )^{\prime }= \alpha \big (1+b(t)\big ) |u|^{\alpha -1}u$ are investigated under a smallness condition and some signum conditions on $b(t)$. When $\alpha =1$, our results reduce to well-known ones for linear ordinary differential equations.
[1] Bodine, S., Lutz, D.A.: Asymptotic Integration of Differential and Difference Equations. Lecture Notes in Math., vol. 2129, Springer, 2015. MR 3362540
[2] Coppel, W.A.: Stability and Asymptotic Behavior of Differential Equations. Heath, 1965. MR 0190463 | Zbl 0154.09301
[3] Došlý, O., Řehák, P.: Half-linear Differential Equations. Elsevier, 2005. MR 2158903
[4] Hartman, P.: Ordinary Differential Equations. Birkhäuser, 1982. MR 0658490 | Zbl 0476.34002
[5] Mizukami, M., Naito, M., Usami, H.: Asymptotic behavior of solutions of a class of second order quasilinear ordinary differential equations. Hiroshima Math. J. 32 (2002), 51–78. DOI 10.32917/hmj/1151007642 | MR 1892669 | Zbl 1017.34053
[6] Naito, Y., Tanaka, S.: Sharp conditions for the existence of sign-changing solutions to equations involving the one-dimensional p-Laplacian. Nonlinear Anal. 69 (2008), 3070–3083. MR 2452116
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