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Asymptotic problems for nonlinear ordinary differential equations with phi-Laplacian

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DOŠLÁ Zuzana FUJIMOTO Kodai

Rok publikování 2020
Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Mathematical Analysis and Applications
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://doi.org/10.1016/j.jmaa.2019.123674
Doi http://dx.doi.org/10.1016/j.jmaa.2019.123674
Klíčová slova Oscillation; Asymptotic behavior; Unbounded solutions; Weakly increasing solutions; Extremal solutions; Prescribed mean curvature equations
Popis This paper deals with the asymptotic problems for the nonlinear differential equation (a(t)phi(x'))' + b(t)vertical bar x vertical bar(gamma) sgn x = 0 involving phi-Laplacian. Necessary and sufficient conditions are given for the oscillation of solutions of this equation. Moreover, we study the existence of unbounded solutions with different asymptotic behavior, in particular, weakly increasing solutions and extremal solutions. Examples for prescribed mean curvature equation are given to illustrate our results. (C) 2019 Elsevier Inc. All rights reserved.
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