Eventually positive solutions for nonlinear impulsive differential equations with delays

Shao Yuan Huang, and Sui Sun Cheng. "Eventually positive solutions for nonlinear impulsive differential equations with delays." Annales Polonici Mathematici 104.1 (2012): 43-70. <http://eudml.org/doc/280685>.

@article{ShaoYuanHuang2012,
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.},
author = {Shao Yuan Huang, Sui Sun Cheng},
journal = {Annales Polonici Mathematici},
keywords = {impulsive differential equation; delay; positive solution; comparison theorem; oscillation criteria},
language = {eng},
number = {1},
pages = {43-70},
title = {Eventually positive solutions for nonlinear impulsive differential equations with delays},
url = {http://eudml.org/doc/280685},
volume = {104},
year = {2012},
}

TY - JOUR
AU - Shao Yuan Huang
AU - Sui Sun Cheng
TI - Eventually positive solutions for nonlinear impulsive differential equations with delays
JO - Annales Polonici Mathematici
PY - 2012
VL - 104
IS - 1
SP - 43
EP - 70
AB - 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.
LA - eng
KW - impulsive differential equation; delay; positive solution; comparison theorem; oscillation criteria
UR - http://eudml.org/doc/280685
ER -