
handle: 10533/177702
The authors establish conditions for the existence of mild and strong solutions of a partial neutral functional-differential equation with unbounded delay of the form \[ (d/dt)(x(t)+F(t, x_t)) = Ax(t)+G(t, x_t) \] subject to pre-assigned moments of impulse effects. Here, \(A\) is the infinitesimal generator of a strongly continuous semigroup of linear operators on a Banach space, \(x_t\) is a Hale-type operator and \(F,G\) are given functions defined on a phase space. They also revisit an example presented in an earlier paper of the authors [J. Math Anal. Appl. 221, No. 2, 452--475 (1998; Zbl 0915.35110)] now considering that impulse conditions are imposed on the system.
Neutral differential equations, Semigroups of bounded linear operators, Impulsive differential equations, Applied Mathematics, semigroups of bounded linear operators, Initial value problems for higher-order parabolic equations, Functional-differential equations with impulses, impulsive differential equations, neutral differential equations
Neutral differential equations, Semigroups of bounded linear operators, Impulsive differential equations, Applied Mathematics, semigroups of bounded linear operators, Initial value problems for higher-order parabolic equations, Functional-differential equations with impulses, impulsive differential equations, neutral differential equations
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