Eventually positive solutions for nonlinear impulsive differential equations with delays

Volume 104 / 2012

Shao Yuan Huang, Sui Sun Cheng Annales Polonici Mathematici 104 (2012), 43-70 MSC: Primary 34K45; Secondary 34K11. DOI: 10.4064/ap104-1-4

Abstract

Several recent oscillation criteria are obtained for nonlinear delay impulsive differential equations by relating them to linear delay impulsive differential equations or inequalities, and then comparison and oscillation criteria for the latter are applied. However, not all nonlinear delay impulsive differential equations can be directly related to linear delay impulsive differential equations or inequalities. Moreover, standard oscillation criteria for linear equations cannot be applied directly since continuous coefficient functions and initial functions are required. Therefore we establish oscillation criteria for linear or nonlinear impulsive equations with piecewise continuous coefficients and initial functions. Our technique is based on transforming our problem into a fixed point problem in Banach spaces, and then establishing comparison theorems. Our results extend, improve and correct some well known results in the literature.

Authors

  • Shao Yuan HuangDepartment of Mathematics
    Tsing Hua University
    Hsinchu, Taiwan 30043
    e-mail
  • Sui Sun ChengDepartment of Mathematics
    Tsing Hua University
    Hsinchu, Taiwan 30043
    e-mail

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