Almost periodic solutions to abstract retarded functional differential equations with unbounded delay
The authors consider quasilinear partial retarded functional-differential equations with unbounded delay of the forms \[ x'= Ax+ F(t, x_t)\quad\text{and}\quad x''= Ax+ F(t,x_t), \] where \(A\) is the infinitesimal generator of a strongly continuous semigroup of linear operators and of a cosine function of linear operators, respectively. The existence of bounded, almost-periodic and asymptotic almost-periodic mild solutions are established.
quasilinear partial retarded functional-differential equations
bounded, almost-periodic and asymptotic almost-periodic mild solutions
scientific article; zbMATH DE number 1385267