文章基本信息

标题：Existence of solutions of multi-point boundary value problems on time scales at resonance
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作者：Junfang Zhao ; Baozeng Chu ; Hairong Lian 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2013
卷号：2013
期号：1
页码：351
DOI：10.1186/1687-1847-2013-351
语种：English
出版社：Hindawi Publishing Corporation
摘要：By applying the coincidence degree theorem due to Mawhin, we show the existence of at least one solution to the nonlinear second-order differential equation u Δ ∇ ( t ) = f ( t , u ( t ) , u Δ ( t ) ) , t ∈ [ 0 , 1 ] T , subject to one of the following multi-point boundary conditions: u ( 0 ) = ∑ i = 1 m α i u ( ξ i ) , u Δ ( 1 ) = 0 , and u ( 0 ) = ∑ i = 1 m α i u ( ξ i ) , u ( 1 ) = 0 , where T is a time scale such that 0 ∈ T , 1 ∈ T k , ξ i ∈ ( 0 , 1 ) ∩ T , i = 1 , 2 , … , m , f : [ 0 , 1 ] T × R 2 → R is continuous and satisfies the Carathéodory-type growth conditions. MSC:34B15, 39A10, 47G20.
关键词：multi-point BVP ; time scale ; resonance ; coincidence degree