INVARIANT STABLE MANIFOLDS FOR  PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH FINITE DELAY

Trinh Xuan Yen; Nguyen Thi Thu Hang

Trinh Xuan Yen Department of Basic Science, Hung Yen University of Technology and Education
Nguyen Thi Thu Hang Department of Basic Science, Hung Yen University of Technology and Education

Keywords: Banach function space, evolution family, exponential dichotomy, manifold

Abstract

We prove the existence of invarinat stable manifolds for the solutions to the equation

in the case where the evolution family (U(t,s))_t≥s≥0has an exponential dichotomy on a half-line, and the nonlinear forcing term g satisfies the -Lipschitz conditions, i.e., , where belongs to some classes of admissible function space. Our main method is based on the addmissibility of function space.

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