Abstract
In this paper, oscillatory and asymptotic property of solutions of a class of nonlinear fourth order neutral dynamic equations of the form ( H ) ( r ( t ) ( y ( t ) + p ( t ) y ( α ( t ) ) ) Δ 2 ) Δ 2 + q ( t ) G ( y ( β ( t ) ) ) = 0 and ( N H ) ( r ( t ) ( y ( t ) + p ( t ) y ( α ( t ) ) ) Δ 2 ) Δ 2 + q ( t ) G ( y ( β ( t ) ) ) = f ( t ) for t ∈ [ t 0 , ∞ ] T , t 0 ⩾ 0 , where T is a time scale such that sup T = ∞ , t 0 ∈ T have been studied under the assumption ∫ t 0 ∞ t r ( t ) Δ t = ∞ for various ranges of p ( t ) . Sufficient conditions are obtained for the existence of bounded positive solutions of ( N H ) by using Schauder’s fixed point theorem.
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