In this paper we study the dependence on a parameter of the periodic solutions of a system of parabolic inclusions of the form (1) yi (t) \in Aiyi + fi(t, y1, . . . , yn), i = 1, . . . , n, where X1, . . . ,Xn are separable Banach spaces, Ai are the generators of analytic semigroups eAit in Xi, i = 1, . . . , n, and fi : R × X1 × . . . × Xn ( Xi, i = 1, . . . , n, are nonlinear multivalued maps which are T-periodic with respect to the first variable. We consider here the case when the analytic semigroups eAit are not compact. We consider two different types of dependence of the right hand side of (1) on a large parameter μ. In both cases the right hand side does not have a limit as μ tends to infinity. We can construct a formal limit of inclusions in such a way that the vector fields whose fixed points represent the periodic solutions of the inclusions depending on the parameter and the vector fields of the limit inclusions are homotopic.
On the periodic solutions problem for parabolic inclusions with a large parameter / M. Kamenski; P. Nistri; P. Zecca. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - STAMPA. - 8:(1996), pp. 57-77.
On the periodic solutions problem for parabolic inclusions with a large parameter
ZECCA, PIETRO
1996
Abstract
In this paper we study the dependence on a parameter of the periodic solutions of a system of parabolic inclusions of the form (1) yi (t) \in Aiyi + fi(t, y1, . . . , yn), i = 1, . . . , n, where X1, . . . ,Xn are separable Banach spaces, Ai are the generators of analytic semigroups eAit in Xi, i = 1, . . . , n, and fi : R × X1 × . . . × Xn ( Xi, i = 1, . . . , n, are nonlinear multivalued maps which are T-periodic with respect to the first variable. We consider here the case when the analytic semigroups eAit are not compact. We consider two different types of dependence of the right hand side of (1) on a large parameter μ. In both cases the right hand side does not have a limit as μ tends to infinity. We can construct a formal limit of inclusions in such a way that the vector fields whose fixed points represent the periodic solutions of the inclusions depending on the parameter and the vector fields of the limit inclusions are homotopic.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.