Existence of positive periodic solutions for evolution equations with delay in ordered Banach spaces

Abstract

The main focus of this study is to discuss the existence of positive ω\omega -periodic mild solutions for evolution equation with delay in an ordered Banach space EE. Under the ordered conditions of the growth exponent of the nonlinearity gg with respect to the semigroup T(t)(t≥0){\mathcal{T}}\left(t)\hspace{.25em}\left(t\ge 0) or the first eigenvalue of the operator A{\mathcal{A}}, the existence results of mild solutions and positive mild solutions for evolution equation are obtained by applying the Poincaré mapping and monotone iterative method, and adding appropriate conditions to the nonlinearity term gg without assuming the existence of upper and lower solutions. Finally, we give an example to verify the applicability of our abstract results.

Keywords

• monotone iterative method
• periodic solutions
• compact semigroup
• poincaré mapping
• positive c 0-semigroup
• evolution equations with delay
• 34g10
• 34k45
• 47d03
• 34k30
• 47h07
• 47h08