We consider the problem of the existence and uniqueness of solutions to a semilinear equation in a Hilbert space, of the type Lu = Nu, where the linear operator L is assumed to be anti-selfadjoint, and the nonlinear part N is controlled by two bounded selfadjoint operators A and B. As an example of application, we study the existence and uniqueness of periodic solutions for a system of transport equations. Precisely, we look for solutions which are periodic in each of their variables, the periods being determined by the forcing term.
Existence and uniqueness of solutions for semilinear equations involving anti-selfadjoint operators
FONDA, ALESSANDRO
2014-01-01
Abstract
We consider the problem of the existence and uniqueness of solutions to a semilinear equation in a Hilbert space, of the type Lu = Nu, where the linear operator L is assumed to be anti-selfadjoint, and the nonlinear part N is controlled by two bounded selfadjoint operators A and B. As an example of application, we study the existence and uniqueness of periodic solutions for a system of transport equations. Precisely, we look for solutions which are periodic in each of their variables, the periods being determined by the forcing term.File in questo prodotto:
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