Classification and existence of positive solutions of fourth-order nonlinear difference equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Classification and existence of positive solutions of fourth-order nonlinear difference equations

Authors:

J. V. Manojlović

Affiliation:

(1) Department of Mathematics and Computer Science, Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia

Abstract:

We consider a class of fourth-order nonlinear difference equations of the form

$(Omega)qquadqquadqquadqquadqquadqquad mathit{Delta}^2 left( {p_n left( {mathit{Delta}^2 y_n } right)^{alpha } } right) + q_n y_{n + 3}^{beta } = 0,quad n in mathbb{N},$

where α and β are the ratios of odd positive integers, and {p _n} and {q _n} are positive real sequences defined for all $n in mathbb{N}left( {n_0 } right)$ satisfying the condition

$sumlimits_{{n = n_0 }}^{infty } {nleft( {frac{n}{{p_n }}} right)^{{{1 mathord{left/ {vphantom {1 alpha }} right. } alpha }}} < infty .}$

We classify the nonoscillatory solutions of (Ω) and establish necessary and/or sufficient conditions for the existence of nonoscillatory solutions with specific asymptotic behavior. Supported by Ministry of Science, Technology and Development of Republic of Serbia – Grant No. 144003.

Keywords:

nonlinear difference equation nonoscillatory solution positive solutions asymptotic behavior classification of solutions oscillation

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