Existence of positive S-asymptotically periodic solutions of the fractional evolution equations in ordered Banach spaces
Qiang Li, Lishan Liu, Mei Wei
Abstract
In this paper, we discuss the asymptotically periodic problem for the abstract fractional evolution equation under order conditions and growth conditions. Without assuming the existence of upper and lower solutions, some new results on the existence of the positive S-asymptotically ω-periodic mild solutions are obtained by using monotone iterative method and fixed point theorem. It is worth noting that Lipschitz condition is no longer needed, which makes our results more widely applicable.
Topics & Concepts
MathematicsMonotone polygonLipschitz continuityFixed-point theoremBanach spaceFixed pointMathematical analysisApplied mathematicsPure mathematicsGeometryNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Numerical Methods