Nonmonotone impulse effects in second-order periodic boundary value problems

Irena Rachůnková and Milan Tvrdý

Abstract and Applied Analysis, 2004, vol. 2004, 1-14

Abstract:

We deal with the nonlinear impulsive periodic boundary value problem u ″ = f ( t , u , u ′ ) , u ( t i + ) = J i ( u ( t i ) ) , u ′ ( t i + ) = M i ( u ′ ( t i ) ) , i = 1 , 2 , … , m , u ( 0 ) = u ( T ) , u ′ ( 0 ) = u ′ ( T ) . We establish the existence results which rely on the presence of a well-ordered pair ( σ 1 , σ 2 ) of lower/upper functions ( σ 1 ≤ σ 2 on [ 0 , T ] ) associated with the problem. In contrast to previous papers investigating such problems, the monotonicity of the impulse functions J i , M i is not required here.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:472191

DOI: 10.1155/S1085337504306299

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