Nonmonotone impulse effects in second‐order periodic boundary value problems

Irena Rachůnková and Milan Tvrdý

Abstract and Applied Analysis, 2004, vol. 2004, issue 7, 577-590

Abstract: We deal with the nonlinear impulsive periodic boundary value problem u″ = f(t, u, u′), u(ti+) = Ji(u(ti)), u′(ti+) = Mi(u′(ti)), 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 (σ1, σ2) of lower/upper functions (σ1 ≤ σ2 on [0, T]) associated with the problem. In contrast to previous papers investigating such problems, the monotonicity of the impulse functions Ji, Mi is not required here.

Date: 2004
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https://doi.org/10.1155/S1085337504306299

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2004:y:2004:i:7:p:577-590

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