Generalized Prüfer angle and oscillation of half-linear differential equations

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• 作者：O. Do&scaron ; lý ; ^a ; J. Jaro&scaron ; ^b ; M. Veselý ; ^a ; ^{xvesely@math.muni.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Prü ; fer angle ; Half-linear equations ; Oscillation theory ; Conditional oscillation ; Oscillation constant
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：64
• 期：Complete
• 页码：34-41
• 全文大小：769 K

文摘

In this paper, we introduce a new modification of the half-linear Prüfer angle. Applying this modification, we investigate the conditional oscillation of the half-linear second order differential equation where w the MathML source">p>1, w the MathML source">α≠p, and w the MathML source">r,s are continuous functions such that w the MathML source">r(t)>0 for large w the MathML source">t. We present conditions on the functions w the MathML source">r,s which guarantee that Eq. (w the MathML source">∗) behaves like the Euler type equation w the MathML source">[t^α−1Φ(x^′)]^′+λt^α−1−pΦ(x)=0, which is conditionally oscillatory with the oscillation constant w the MathML source">λ₀=|p−α|^p∕p^p.