Oscillation constants for Euler type differential equations involving the p(t)-Laplacian

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:470

Article

Fujimoto, Kodai¹  Yamaoka, Naoto¹ 

[1] Osaka Prefecture Univ, Dept Math Sci, Sakai, Osaka 5998531, Japan

关键词: Oscillation theory;    Oscillation constant;    p(t)-Laplacian;    Half-linear differential equation;    Riccati technique;   

DOI  :  10.1016/j.jmaa.2018.10.063

来源: Elsevier

【 摘 要 】

This paper deals with the oscillation problem for the nonlinear differential equation (vertical bar x'vertical bar(p(t)-2)x')' + lambda/t(p(t))vertical bar x vertical bar(p(t)-2)x = 0, where lambda is a positive parameter and p(t) > 1 is a nondecreasing and smooth function. Some (non)oscillation criteria are given for this equation. The obtained results are the best possible in a certain sense. We use the Riccati technique and the function sequence technique. Moreover, we propose a conjecture concerning the oscillation problem for this equation in the case when p(t) tends to infinity as t -> infinity. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free