Differential equations of even-order with p -Laplacian like operators: qualitative properties of the solutions

Advances in Difference Equations

article

Bazighifan, Omar¹  Abdeljawad, Thabet³  Al-Mdallal, Qasem M.⁶ 

[1] Department of Mathematics, Faculty of Science, Hadhramout University;Department of Mathematics, Faculty of Education, Seiyun University;Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University;Department of Mathematical Sciences, United Arab Emirates University

关键词: Even-order;    Differential equation;    Oscillation;    p -Laplacian equation;   

DOI  :  10.1186/s13662-021-03254-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we study the oscillation of solutions for an even-order differential equation with middle term, driven by a p-Laplace differential operator of the form$$ \textstyle\begin{cases} ( r ( x ) \Phi _{p}[z^{ ( \kappa -1 ) } ( x ) ] ) ^{\prime }+a ( x ) \Phi _{p}[f ( z^{ ( \kappa -1 ) } ( x ) ) ]+ \sum_{i=1}^{j}q_{i} ( x ) \Phi _{p}[h ( z ( \delta _{i} ( x ) ) ) ]=0, \\ \quad j\geq 1, r ( x ) >0, r^{\prime } ( x ) +a ( x ) \geq 0, x\geq x_{0}>0. \end{cases}$$ The oscillation criteria for these equations have been obtained. Furthermore, an example is given to illustrate the criteria.

【 授权许可】

CC BY