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Stepanov-like pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations

2011; Elsevier BV; Volume: 75; Issue: 1 Linguagem: Inglês

10.1016/j.na.2011.08.026

1873-5215

Zhanrong Hu, Zhen Jin,

Differential Equations and Numerical Methods

We obtain new existence and uniqueness theorems of pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations ddt[u(t)+f(t,u(t))]=A(t)[u(t)+f(t,u(t))]+g(t,u(t)),t∈R,ddt[u(t)+f(t,Bu(t))]=A(t)[u(t)+f(t,Bu(t))]+g(t,Cu(t)),t∈R, assuming that A(t) satisfy “Acquistapace–Terreni” conditions, the evolution family generated by A(t) has exponential dichotomy, R(λ0,A(⋅)) is almost periodic, B,C are densely defined closed linear operators, f,g are Lipschitz with respect to the second argument uniformly in the first argument, f is pseudo almost periodic in the first argument, g is Stepanov-like pseudo almost periodic in the first argument for p>1 and jointly continuous. To illustrate our abstract results, two examples are given.