Abstract
We prove the existence of mild and strong solutions of integrodifferential equations with nonlocal conditions in Banach spaces. Further sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed‐point theorem. Examples are provided to illustrate the theory.
Highlights
Byszewski [9] has studied the existence and uniqueness of mild, strong, and classical solutions of the following nonlocal Cauchy problem: du(t) dt + Au(t) =f t,u(t), t ∈ (0, a], u t0 + g t1, t2, . . . , tp, u(·) = u0, (1.1) (1.2)where 0 ≤ t0 < t1 < · · · < tp ≤ a, a > 0, −A is the infinitesimal generator of a C0-semigroup in a Banach space X, u0 ∈ X, and f : [0, a] × X → X, g : [0, a]p × X → X are given functions
Where 0 ≤ t0 < t1 < · · · < tp ≤ a, a > 0, −A is the infinitesimal generator of a C0-semigroup in a Banach space X, u0 ∈ X, and f : [0, a] × X → X, g : [0, a]p × X → X are given functions
Ntouyas and Tsamatos [31] have established the global existence of solutions of semilinear evolution equations with nonlocal conditions
Summary
Byszewski [9] has studied the existence and uniqueness of mild, strong, and classical solutions of the following nonlocal Cauchy problem: du(t) dt. Balachandran [1], Balachandran and Ilamaran [6], Balachandran and Chandrasekaran [3], Dauer and Balachandran [17], and Balachandran et al [7] have studied the nonlocal Cauchy problem for various classes of integrodifferential equations. Physical motivation for this kind of problem is given in [18, 25].
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