The paper deals with the existence of a local solution and some qualitative properties of the set of solutions for the following Cauchy problem governed by an evolution inclusion of subdifferential type. Based on a stability result with respect to the initial value and to a multimap-perturbation, a local existence result is proved using a fixed point technique. The next theorem of the paper concerns a convergence result. From here the authors prove that the multifunction which assigns to an initial value the set of solutions is upper semicontinuous with respect to the Hausdorff metric. In the last part of the paper the above-mentioned results are used to investigate some properties of the solutions to a multivalued problem. The paper extends some earlier results by G. Colombo and M. Tosques [Ann. Mat. Pura Appl. (4) 160 (1991), 147–162 (1992)] and by the authors.
Convergence results for nonlinear evolution inclusions
CARDINALI, Tiziana;
1995
Abstract
The paper deals with the existence of a local solution and some qualitative properties of the set of solutions for the following Cauchy problem governed by an evolution inclusion of subdifferential type. Based on a stability result with respect to the initial value and to a multimap-perturbation, a local existence result is proved using a fixed point technique. The next theorem of the paper concerns a convergence result. From here the authors prove that the multifunction which assigns to an initial value the set of solutions is upper semicontinuous with respect to the Hausdorff metric. In the last part of the paper the above-mentioned results are used to investigate some properties of the solutions to a multivalued problem. The paper extends some earlier results by G. Colombo and M. Tosques [Ann. Mat. Pura Appl. (4) 160 (1991), 147–162 (1992)] and by the authors.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
