On a class of second-order impulsive boundary value problem at resonance

Guolan Cai, Zengji Du and Weigao Ge

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-11

Abstract:

We consider the following impulsive boundary value problem, x ″ ( t ) = f ( t , x , x ′ ) , t ∈ J \ { t 1 , t 2 , … , t k } , Δ x ( t i ) = I i ( x ( t i ) , x ′ ( t i ) ) , Δ x ′ ( t i ) = J i ( x ( t i ) , x ′ ( t i ) ) , i = 1 , 2 , … , k , x ( 0 ) = ( 0 ) , x ′ ( 1 ) = ∑ j = 1 m − 2 α j x ′ ( η j ) . By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than recent results. Our results extend some work concerning the usual m -point boundary value problem at resonance without impulses.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:062512

DOI: 10.1155/IJMMS/2006/62512

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