Sufficient Conditions for Oscillation of Fourth-Order Neutral Differential Equations with Distributed Deviating Arguments

Axioms

Feliz Minhos¹  Omar Bazighifan²  Osama Moaaz³ 

[1] Departamento de Matematica, Escola de Ciencias e Tecnologia, Centro de Investigacao em Matematica e Aplicacoes (CIMA), Instituto de Investigacao e Formacao Avancada, Universidade de Evora, Rua Romao Ramalho, 59, 7000-671 Evora, Portugal;Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen;Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt;

关键词: fourth-order differential equations;    neutral delay;    oscillation;   

DOI  :  10.3390/axioms9020039

来源: DOAJ

【 摘 要 】

Some new sufficient conditions are established for the oscillation of fourth order neutral differential equations with continuously distributed delay of the form ${\left(r\left(t\right){\left(N_x^{\prime \prime \prime }\left(t\right)\right)}^{\alpha }\right)}^{\prime }+{\int }_a^{b}q\left(t,\vartheta \right)x^{\beta }\left(\delta \left(t,\vartheta \right)\right)d\vartheta =0,$ where $t\ge t_0$ and $N_x\left(t\right):=x\left(t\right)+p\left(t\right)x\left(\phi \left(t\right)\right)$ . An example is provided to show the importance of these results.

【 授权许可】

Unknown