Existence of solutions for a class of second-order impulsive Hamiltonian system with indefinite linear part

Zhang, Qiongfen

doi:10.22436/jnsa.011.03.05

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2018

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“…where a(t), b(t), and g(t) are allowed to change sign on [0, 1]. For the latest results of indefinite problems, please refer to Jiao and Zhang [68], Feltrin and Sovrano [69], and Zhang [70].…”

Section: Introductionmentioning

confidence: 99%

A class of second-order nonlocal indefinite impulsive differential systems

Jiao

Zhang

2018

Bound Value Probl

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1 0 g(t)y(t) dt, y (1) = 0, where the weight functions a(t), b(t), and ω(t) change sign on [0, 1], and g(t) ≡ 0 and h(t) ≡ 0 on [0, 1]. By constructing a cone K 1 × K 2 , which is the Cartesian product of two cones in space PC[0, 1], and applying the well-known fixed point theorem of cone expansion and compression in K 1 × K 2 , we obtain conditions for the existence and multiplicity of positive solutions of a nonlocal indefinite impulsive differential system. An example is given to illustrate the main results.

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Section: Introductionmentioning

confidence: 99%