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Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces

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  • Aneta Sikorska-Nowak
  • Grzegorz Nowak

Abstract

We prove two existence theorems for the integrodifferential equation of mixed type: x ' ( t ) = f ( t , x ( t ) , ∫ 0 t k 1 ( t , s ) g ( s , x ( s ) ) d s , ∫ 0 a k 2 ( t , s ) h ( s , x ( s ) ) d s ) , x ( 0 ) = x 0 , where in the first part of this paper f , g , h , x are functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil (HK). In the second part f , g , h , x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functions f , g , h , x satisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.

Suggested Citation

  • Aneta Sikorska-Nowak & Grzegorz Nowak, 2007. "Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-14, September.
    • Handle: RePEc:hin:jijmms:065947
    DOI: 10.1155/2007/65947
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