MR3099035
Ravi P. AGARWAL and Jelena V. MANOJLOVIĆ
Ravi P. AGARWAL and Jelena V. MANOJLOVIĆ
On the Existence and the Asymptotic Behavior of Nonoscillatory Solutions of Second Order Quasilinear Difference Equations
Funkcialaj Ekvacioj. Serio Internacia
56
2013
81--109
http://fe.math.kobe-u.ac.jp/FE/FullPapers/56-1/56_81.pdf
http://www.ams.org/mathscinet-getitem?mr=MR3099035
For the second-order quasilinear difference equation $\Delta(p_n|\Delta x_n|^{\alpha-1}\Delta x_n) + q_n|x_{n+1}|^{\beta-1}x_{n+1} = 0$, $\alpha>\beta$, we establish a necessary and sufficient condition for the existence of slowly growing and slowly decaying positive solution. In particular, when $p_n=1$, the precise asymptotic forms of its slowly growing positive solutions are obtained.
Emden-Fowler difference equations, Asymptotic behavior of solutions, Positive solutions, Slowly growing solutions, Slowly decaying solutions, Regularly varying functions, Slowly varying functions.
26A12, 39A12, 39A22.
56-81
2013
On the Existence and the Asymptotic Behavior of Nonoscillatory Solutions of Second Order Quasilinear Difference Equations
Ravi P. AGARWAL and Jelena V. MANOJLOVIĆ
Ravi P. AGARWAL and Jelena V. MANOJLOVIĆ
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