English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Some oscillation criteria for the half-linear Emden-Fowler functional differential equations of neutral type of the form                     1 1 0 , r t z t z t q t x t x t e t t t             are established, where           , , 0 0 z t x t p t x t        are arbitrary constants, some earlier results are the special cases of ours since the function   e t is introduced to the equation. Introduction This paper consider half-linear Emden-Fowler functional differential equations of neutral type                     1 1 0 , , r t z t z t q t x t x t e t t t             (1.1) where           , 0, 0 z t x t p t x t        . The following conditions are always valid, if not stated.         1 1 0 ( ) [ t , ), , 0 , 0. A r t C R r t r t              2 0 ( ), ( ) [ t , ), , 0 1, 0. A p t q t C R p t q t                3 0 [ t , ), , , lim . t A t C R t t t                        1 4 0 [ t , ), , 0, 0, , lim . t A t C R t t t t t                     1 5 0 ( ) [ t , ), , 0 . A e t C R e t    Definition The function     1 ( ) , , , x x t C T R   0 , x T t  is called a solution of the equation (1.1), if it has the properties of         1 1 ( ) , , x r t z t z t C T R      , and it satisfies the equation in   , x T  , moreover if it has arbitrarily large zeros for x T T  , then we call ( ) x t is a oscillatory solution of equation (1.1), otherwise it is called nonoscillatory. If each solution of (1.1) is oscillatory, we call equation (1.1) is oscillatory. This paper only consider the non-trivial solution of equation (1.1).

Oscillation Criteria for a Class of Certain Half-linear Emden-Fowler Functional Differential Equations of Neutral Type