Alternative theorems for pseudo almost automorphic problems (Q636061)

The paper gives alternative theorems to investigate the existence of pseudo almost automorphic solutions for semilinear evolution equations \(\frac{du}{dt}=A(t)u(t)+f(t,u)+\lambda g(t,u)\), \(t\in {\mathbb R}\), \(\lambda\in[0,1]\) in a Banach space \(X\). It is assumed that the linear operators \(A(t)\) satisfy some conditions, and \(f,g:{\mathbb R}\times X \rightarrow X\) are pseudo almost automorphic in \(t\) uniformly for \(x\in X\). As an illustration of the results, a parabolic equation is considered.