Krasnosel'skii type formula and translation along trajectories method on the scale of fractional spaces

2014/04/13 by Piotr Kokocki, Kokocki, Piotr
Mathematics · #35B10 #37L05 #47J35 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Nonlinear Differential Equations Analysis #math.DS #msc:35B10 #msc:37L05 #msc:47J35

paper · pdf · doi:10.48550/arxiv.1404.3431

20 pages

openalex publication_date 2014/04/13 · arxiv created 2015/10/30 · arxiv updated 2015/11/02 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We provide global continuation principle of periodic solutions for the equation u = - Au + F(t,u), where A:D(A)→ X is a sectorial operator on a Banach space X and F:[0,+∞)× X^α→ X is a nonlinear map defined on fractional space X^α. The approach that we use in this paper is based upon the theory of topological invariants that applies in the situation when Poincaré operator associated with the equation is endowed with some form of compactness.

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