A two-points boundary value problem associated to a semilinear multivalued evolution equation is investigated, in reflexive and separable Banach spaces. To this aim, an original method is proposed based on the use of weak topologies and on a suitable continuation principle in Fr\'echet spaces. Liapunov-like functions are introduced, for proving the required transversality condition. The linear part can also depend on the state variable and the discussion comprises the cases of a nonlinearity with sublinear growth in or of a noncompact valued one. Some applications are given, to the study of periodic boundary value problems of partial differential inclusions. Comparisons are included, with recent related achievements.
Two-points b.v.p. for multivalued equations with weakly regular r.h.s.
BENEDETTI, Irene;
2011
Abstract
A two-points boundary value problem associated to a semilinear multivalued evolution equation is investigated, in reflexive and separable Banach spaces. To this aim, an original method is proposed based on the use of weak topologies and on a suitable continuation principle in Fr\'echet spaces. Liapunov-like functions are introduced, for proving the required transversality condition. The linear part can also depend on the state variable and the discussion comprises the cases of a nonlinearity with sublinear growth in or of a noncompact valued one. Some applications are given, to the study of periodic boundary value problems of partial differential inclusions. Comparisons are included, with recent related achievements.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
