Belkacem Chaouchi, Marko Kostić

Periodic Solutions for Fourth-Order Differential Evolution Equation Involving Poly-Harmonic Operator

abstract:
In this note, we analyze the existence and uniqueness of periodic solutions for a fourth-order evolution differential equation involving the well known poly-harmonic operator. The right-hand term of the equation is taken in some anistropic Hölder spaces. Our approach is based on the study of a fourth-order abstract differential equation. To this end, we opt for the use of analytic semigroup's techniques.

Mathematics Subject Classification: 34G10, 34K10, 44A45, 47D06, 47G20

Key words and phrases: Abstract differential equations, Hölder spaces, periodic functions