Oscillation of solutions of third order nonlinear neutral differential equations

Advances in Difference Equations

article

Sallam, Ragaa A.¹  Salem, Shaimaa¹  El-Sheikh, Mohamed M. A.¹ 

[1] Department of Mathematics and Computer Science, Faculty of Science, Menoufia University

关键词: Oscillation;    Third order differential equation;    Nonlinear neutral equation;    Nonoscillation;   

DOI  :  10.1186/s13662-020-02777-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The main objective of this article is to improve and complement some of the oscillation criteria published recently in the literature for third order differential equation of the form $$ \bigl( r(t) \bigl( z^{\prime \prime }(t) \bigr) ^{\alpha } \bigr) ^{\prime }+q(t)f \bigl(x \bigl(\sigma (t) \bigr) \bigr)=0,\quad t\geq t_{0}>0, $$ where $z(t)=x(t)+p(t)x(\tau (t))$ and α is a ratio of odd positive integers in the two cases $\int _{t_{0}}^{\infty }r^{\frac{-1}{\alpha } }(s)\,\mathrm {d}s<\infty $ and $\int _{t_{0}}^{\infty }r^{\frac{-1}{\alpha } }(s)\,\mathrm {d}s=\infty $. Some illustrative examples are presented.

【 授权许可】

CC BY