CONDITIONS FOR EXISTENCE OF SOLUTIONS FOR PARTIAL FUNCTIONAL DELAY DIFFERENTIAL EQUATIONS ON A HALF-LINE
Abstract
For the following class of partial functional delay differential equations
we establish the existence and bounded conditions of solutions. In the case of its linear part, the family operators (B(t))t≥0, generates the evolution family (U(t,s))t≥s≥0 (on Banach space X) having an exponential dichotomy on the half-line and the nonlinear forcing delay term f satisfes the 
-Lipschitz condition, i.e., ‖g(t,ut) - g(t,vt)‖C ≤ 
‖ut - vt‖C where ut, vt ∈ C := C([-r,0],X), and 
belongs to an admissible function space on the half-line. Our main method is based on the admissibility of function spaces and fixed point arguments.
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