(μ, ν)-Pseudo almost automorphic solutions for some non-autonomous differential equations

The aim of this work is to study the new concept of the (μ, ν)-pseudo almost automorphic functions for some non-autonomous differential equations. We suppose that the linear part has an exponential dichotomy. The nonlinear part is assumed to be (μ, ν)-pseudo almost automorphic. We show some results regarding the completness and the invariance of the space consisting in (μ, ν)-pseudo almost automorphic functions. Then we propose to study the existence of (μ, ν)-pseudo almost automorphic solutions for some differential equations involving reflection of the argument.