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Almost automorphic solutions for hyperbolic semilinear evolution equations. (English) Zbl 1086.34052

Summary: Here, we deal with mild solutions for the semilinear evolution equation

d dtx(t)=Ax(t)+f(t,x(t)),t,

under the sectoriality of A, a linear operator with not necessarily dense domain, in a Banach space X and σ(A)i=. We discuss the existence and uniqueness of an almost automorphic solution in an intermediate space X α , when the function f:×X α X is almost automorphic. An example illustrating the obtained result is given (a partial differential equation).

MSC:
34G20Nonlinear ODE in abstract spaces
47A55Perturbation theory of linear operators