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) --- 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 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.
A unified approach to some classes of evolution equations and systems with nonlocal conditions
CARDINALI, Tiziana;RUBBIONI, Paola
2014
Abstract
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) --- 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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
