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Eventually positive solutions for nonlinear impulsive differential equations with delays

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Huang S., Cheng S.

Annales Polonici Mathematici

2012

tom 104

nr 1

43-70

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.

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1 Annales Polonici Mathematici

1 Cheng S.

1 Huang S.

1 2012

Wyniki wyszukiwania

Eventually positive solutions for nonlinear impulsive differential equations with delays