A symmetric solution of a multipoint boundary value problem at resonance

Nickolai Kosmatov

Abstract and Applied Analysis, 2006, vol. 2006, 1-11

Abstract:

We apply a coincidence degree theorem of Mawhin to show the existence of at least one symmetric solution of the nonlinear second-order multipoint boundary value problem u ″ ( t ) = f ( t , u ( t ) , | u ′ ( t ) | ) , t ∈ ( 0 , 1 ) , u ( 0 ) = ∑ i = 1 n μ i u ( ξ i ) , u ( 1 − t ) = u ( t ) , t ∈ [ 0 , 1 ] , where 0 < ξ 1 < ξ 2 < … < ξ n ≤ 1 / 2 , ∑ i = 1 n μ i = 1 , f : [ 0 , 1 ] × ℝ 2 → ℝ with f ( t , x , y ) = f ( 1 − t , x , y ) , ( t , x , y ) ∈ [ 0 , 1 ] × ℝ 2 , satisfying the Carathéodory conditions.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:054121

DOI: 10.1155/AAA/2006/54121

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