On Periodic Solutions To Nonlinear Differential Equations In Banach Spaces

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Cavus A. , Khadjiev D., Ozturk S.

FILOMAT, cilt.30, ss.1069-1076, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 30 Konu: 4
  • Basım Tarihi: 2016
  • Doi Numarası: 10.2298/fil1604069c
  • Dergi Adı: FILOMAT
  • Sayfa Sayıları: ss.1069-1076


Let A denote the generator of a strongly continuous periodic one-parameter group of bounded linear operators in a complex Banach space H. In this work, an analog of the resolvent operator which is called quasi-resolvent operator and denoted by R-lambda is defined for points of the spectrum, some equivalent conditions for compactness of the quasi-resolvent operators R-lambda are given. Then using these, some theorems on existence of periodic solutions to the non-linear equations Phi(A)x = f (x) are given, where Phi(A) is a polynomial of A with complex cofficients and f is a continuous mapping of H into itself.