Almost Automorphic Solutions to Integral Equations on the Line
نویسندگان
چکیده
Given a ∈ L(R) and A the generator of an L-integrable family of bounded and linear operators defined on a Banach space X, we prove the existence of almost automorphic solution to the semilinear integral equation u(t) = ∫ t −∞ a(t − s)[Au(s) + f(s, u(s))]ds for each f : R × X → X almost automorphic in t, for each x ∈ X, and satisfying diverse Lipschitz type conditions. In the scalar case, we prove that a ∈ L(R) positive, nonincreasing and log-convex is already sufficient.
منابع مشابه
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