Schaefer type theorem and periodic solutions of evolution equations
By Yicheng Liu, Zhixian Li. 2006
52 citations recorded by the source corpus.
Abstract Two fixed point theorems for the sum of contractive and compact operators are obtained in this paper, which generalize and improve the corresponding results in [H. Schaefer, Uber die methode der a priori-Schranken, Math. Ann. 129 (1955) 415–416; T.A. Burton, Integral equations, implicit functions and fixed points, Proc. Amer. Math. Soc. 124 (1996) 2383–2390; V.I. Istrǎtescu, Fixed Point Theory, an Introduction, Reidel, Dordrecht, 1981; T.A. Burton, K. Colleen, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 23–31; D.R. Smart, Fixed Point Theorems, Cambridge Univ. Press, Cambridge, 1980]. As the applications for the results, we obtain the existence of periodic solutions for some evolution equations with delay, which extend the corresponding results in [T.A. Burton, B. Zhang, Periodic solutions of abstract differential equations with infinite delay, J. Differential Equations 90 (1991) 357–396].
Subfields: Applied Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/5abd94a88c209fd7e77be5de333ea7a2629b6b6f
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In Applied Mathematics
In Geometry and Topology
In Numerical Analysis
Citations in the corpus
- Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness (2012, background): “Now, we face the concept of separate contraction mapping which was introduced in [20].”