Cung The Anh, Le Van Hieu
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
| Le Van Hieu |
Academy of Journalism and Communication
36 Xuan Thuy, Cau Giay, Hanoi, Vietnam
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