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| We present the study of the existence of global solutions for a general semilinear evolution equation in a Banach space $X$ under the effect of a nonlocal condition expressed by a linear continuous mapping $F:C([0,a];X)\to X$.
A transition from Volterra to Fredholm integral operator associated to the problem appears as a consequence of the specific nature of the nonlocal map $F$.
Further, both the classical Cauchy problem and the Byszewski one, where the nonlocal condition is dissipated on the entire interval $[0,a]$, are recovered as special cases.
Thanks to a matrix approach, the results are extended to systems of equations in such a way that the system nonlinearities behave independently as much as possible. |
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