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Schaefer type theorem and periodic solutions of evolution equations
- Source :
-
Journal of Mathematical Analysis & Applications . Apr2006, Vol. 316 Issue 1, p237-255. 19p. - Publication Year :
- 2006
-
Abstract
- 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, Über 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]. [Copyright &y& Elsevier]
- Subjects :
- *DIFFERENTIAL equations
*MATHEMATICAL functions
*FIXED point theory
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 316
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 19168325
- Full Text :
- https://doi.org/10.1016/j.jmaa.2005.04.045