Cung The Anh, Le Van Hieu
Abstract:
Using the Contraction Mapping Principle, we study the existence, uniqueness,
and uniform asymptotic stability of solutions to an abstract differential
equation with infinite delay of the form
,
where A is a positive sectorial operator and the nonlinear part B
is Lipschitz continuous with respect to a fractional power of A in the
second variable and the Lipschitz coefficient may depend on time t.
Some special cases and examples are provided to illustrate the results
obtained.
Submitted June 3, 2011. Published March 29, 2012.
Math Subject Classifications: 35B35, 37L15.
Key Words: Infinite delay; sectorial operator; mild solution;
uniform asymptotic stability; fixed point method.
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Cung The Anh Department of Mathematics Hanoi National University of Education 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam email: anhctmath@hnue.edu.vn | |
Le Van Hieu Academy of Journalism and Communication 36 Xuan Thuy, Cau Giay, Hanoi, Vietnam email: hieulv@ajc.edu.vn |
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