Contraction Mapping and stability in an integro-differential equation of nonconvolution type
Document Type
Article
Publication Date
1-1-2014
Abstract
In this paper, we consider a scalar integro-differential equation of nonconvolution type x?=- ?t-rt a(t,s)g(x(s))ds and give conditions on a and g to ensure that the zero solution is asymptotically stable by applying the Contraction Mapping Principle. These conditions do not require a fixed sign of the coefficient function a(t,s), nor do they involve the sign of any derivative of a(t,s). An asymptotic stability theorem with a necessary and sufficient condition is proved.
Recommended Citation
Zhang, Bo, "Contraction Mapping and stability in an integro-differential equation of nonconvolution type" (2014). College of Health, Science, and Technology. 335.
https://digitalcommons.uncfsu.edu/college_health_science_technology/335