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Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations. (English) Zbl 1329.34105
Summary: We present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of $$\mu$$-pseudo almost periodic and $$\mu$$-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov $$\mu$$-pseudo almost periodic terms. An example is shown to illustrate our results.
##### MSC:
 34G20 Nonlinear differential equations in abstract spaces 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations 47A45 Canonical models for contractions and nonselfadjoint linear operators 47D06 One-parameter semigroups and linear evolution equations 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions 37C60 Nonautonomous smooth dynamical systems
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