Uniform attractors of nonclassical diffusion equations on ℝN with memory and singularly oscillating external forces

In this paper, we consider a class of nonclassical diffusion equations on with hereditary memory, in presence of singularly oscillating external forces depending on a positive parameter ε and a new class of nonlinearities, which have no restriction on the upper growth of the nonlinearity. Under a general assumption on the memory kernel κ and for a very large class of nonlinearities, we prove the existence of uniform attractors in . The uniform boundedness (w.r.t. ε) and the convergence of uniform attractors as ε tends to 0 are also studied. Our results extend and improve some results in Anh and Toan.