Periodic solutions for abstract operator equations

On Periodic Solutions of Abstract Differential Equations

Existence of Periodic Positive Solutions for Abstract Difference Equations

has been considered. To the best of our knowledge, however, little has been done for the abstract difference equations see 7–9 . In this note, we will consider this problem. To this end, let X be a real Banach space and let K ⊂ X be a cone, then a Banach space X with a partial ordering ≤ induced by a coneK is called an ordered Banach space. On the other hand, we will denote the identity operato...

Periodic Wave Shock solutions of Burgers equations

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

Periodic solutions for evolution equations ∗

We study the existence and uniqueness of periodic solutions for evolution equations. First we analyze the one-dimensional case. Then for arbitrary dimensions (finite or not), we consider linear symmetric operators. We also prove the same results for non-linear sub-differential operators A = ∂φ where φ is convex.

Existence of Periodic and Almost Periodic Solutions of Abstract Retarded Functional Difference Equations in Phase Spaces