In this work, we establish the existence of mild solutions for a class of impulsive neutral funct... more In this work, we establish the existence of mild solutions for a class of impulsive neutral functional differential equations described by (1.1) (1.2) (1.3)u 0 =φ∈B, where A(t):D⊂X→X is a family of densely defined closed linear operators; (X,‖⋅‖) is a Banach space; I is an interval of ...
Given a∈L 1(ℝ) and A the generator of an L 1-integrable family of bounded and linear operators de... more Given a∈L 1(ℝ) and A the generator of an L 1-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, uniformly in x∈X, and satisfying diverse Lipschitz type conditions. In the scalar case, we prove that a∈L 1(ℝ) positive, nonincreasing and log-convex is already sufficient.
In this work, we establish the existence of mild solutions for a class of impulsive neutral funct... more In this work, we establish the existence of mild solutions for a class of impulsive neutral functional differential equations described by (1.1) (1.2) (1.3)u 0 =φ∈B, where A(t):D⊂X→X is a family of densely defined closed linear operators; (X,‖⋅‖) is a Banach space; I is an interval of ...
Given a∈L 1(ℝ) and A the generator of an L 1-integrable family of bounded and linear operators de... more Given a∈L 1(ℝ) and A the generator of an L 1-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, uniformly in x∈X, and satisfying diverse Lipschitz type conditions. In the scalar case, we prove that a∈L 1(ℝ) positive, nonincreasing and log-convex is already sufficient.
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Papers by Claudio Cuevas