Existence and uniqueness of solutions for semilinear equations involving anti-selfadjoint operators

  • Alessandro Fonda

    Università di Trieste, Italy

Abstract

We consider the problem of the existence and uniqueness of solutions to a semilinear equation in a Hilbert space, of the type , where the linear operator is assumed to be anti-selfadjoint, and the nonlinear part N is controlled by two bounded selfadjoint operators and . 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.

Cite this article

Alessandro Fonda, Existence and uniqueness of solutions for semilinear equations involving anti-selfadjoint operators. Port. Math. 71 (2014), no. 3/4, pp. 183–192

DOI 10.4171/PM/1949