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SOLUTIONS OF NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS IN $L^p$ SPACES

SOLUTIONS OF NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS IN $L^p$ SPACES

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Let X be a real Banach space with norm ∥ㆍ∥. Let T > 0, r ≥a be fixed constants. We denote by L/sup p/ the usual L/sup p/( -r, 0; X) with norm ∥ㆍ∥/sub p/ for 1 ≤p < ∞. Our object is to study the existence of solutions of nonlinear functional evolution equations of the type (FDE) x'(t) + A(t)x(t) = G(t, x/sub t/), 0 ≤t ≤T, x/sub 0/ = ø.(omitted)

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