文章基本信息

标题：Transformation technique, fixed point theorem and positive solutions for second-order impulsive differential equations with deviating arguments
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作者：Xuemei Zhang ; Meiqiang Feng
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：312
DOI：10.1186/1687-1847-2014-312
语种：English
出版社：Hindawi Publishing Corporation
摘要：This paper investigates the boundary value problems of second-order impulsive differential equations with deviating arguments { x ″ ( t ) + ω ( t ) f ( t , x ( α ( t ) ) ) = 0 , t ∈ J , t ≠ t k , x ( t k + ) − x ( t k ) = c k x ( t k ) , k = 1 , 2 , … , n , a x ( 0 ) − b x ′ ( 0 ) = a x ( 1 ) − b x ′ ( 1 ) = ∫ 0 1 h ( s ) x ( t ) d t , where { c k } is a real sequence with c k > − 1 , k = 1 , 2 , … , n , ω may be singular at t = 0 and/or t = 1 . Several new and more general results are obtained for the existence of positive solutions for the above problem by using transformation technique and Krasnosel’skii’s fixed point theorem. We discuss our problems under two cases when the deviating arguments are delayed and advanced. The approach to deal with the impulsive term is different from earlier approaches. It is the first paper where the transformation technique and a fixed point theorem for cones are applied to second-order differential equations with impulsive effects and deviating arguments. An example is included to verify the theoretical results.
关键词：advanced and delayed arguments ; impulsive differential equations ; transformation technique ; fixed point theorem ; positive solutions