PSEUDO S-ASYMPTOTICALLY (ω,c)-PERIODIC SEQUENTIAL SOLUTIONS TO SOME SEMILINEAR DIFFERENCE EQUATIONS IN BANACH SPACES

The main purpose of this paper is to investigate some existence results for pseudo S-asymptotically (ω,c)-periodic sequential solutions to a semilinear difference equation of convolution type and a semilinear Weyl-like fractional difference equation in Banach spaces. For this purpose, we first give the definition of the pseudo S-asymptotically (ω,c)-periodic sequence and prove the completeness, convolution and superposition theorems for such a sequence in abstract spaces. We show some existence and uniqueness of pseudo S-asymptotically (ω,c)-periodic sequential solutions under some different Lipschitz type conditions of the nonlinear force term with its second variable. We also consider the existence of pseudo S-asymptotically (ω,c)-periodic sequential solutions under a non-Lipschitz growth condition.