Existence of a Mild Solution to a Second-Order Impulsive Functional-Differential Equation with a Nonlocal Condition
Many evolutionary processes in nature are characterized by the fact that at certain instants of time they experience a rapid change of their states. The theory of the impulsive differential equations is one of the attractive branches of differential equations which has extensive realistic mathematical modelling applications in physics, chemistry, engineering, and biological and medical sciences. (413.0Kb)
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An abstract second-order semilinear functional-differential equation such that the linear part of its right-hand side is given by the infinitesimal generator of a strongly continuous cosine family of bounded linear operators, and provided with impulse and nonlocal conditions is studied. Under not too restrictive conditions the existence of a mild solution is proved using Schauder’s fixed point theorem. 2010 Mathematics Subject Classification: 34A37, 34G20.